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Artykuły w czasopismach na temat „Auxiliary variable”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 17 czerwca 2025

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Kaur, Harinder, and M. K Sharma. "Efficient Estimators of Population Variance Using Known Population Mode & Variance of Auxiliary Variable." International Journal of Scientific Engineering and Research 4, no. 10 (2016): 108–16. https://doi.org/10.70729/ijser151036.

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Cabrera-Álvarez, Pablo. "Datos agregados para corregir los sesgos de no respuesta y de cobertura en encuestas." Empiria. Revista de metodología de ciencias sociales, no. 49 (December 30, 2020): 39. http://dx.doi.org/10.5944/empiria.49.2021.29231.

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En las últimas décadas la incidencia creciente de los sesgos de no respuesta y cobertura en las encuestas han puesto en entredicho la capacidad de inferir los resultados a la población. Una forma extendida de corregir los sesgos de no respuesta y cobertura en las encuestas es el uso de ponderaciones que equilibran la muestra final de entrevistados. La construcción de ponderaciones requiere información auxiliar, totales poblacionales que estén disponibles para los que responden y para los que no cooperan. En este trabajo, a partir de simulaciones estadísticas, se comprueba la capacidad de la información agregada para corregir el sesgo de no respuesta. Para ello se comparan el ajuste con datos individuales y el sistema de datos agregados, dando como resultado que el uso de datos agregados puede ser útil si se cumplen tres requisitos: 1) la variable estimada está agrupada, 2) la variable estimada y la auxiliar están correlacionadas y 3) la probabilidad de completar la encuesta está relacionada con la variable auxiliar.In the last decades the effect of nonresponse and coverage bias in surveys have questioned the ability of inferring the results to the population. An extended procedure used to correct nonresponse and coverage problems is the use of weights to balance the sample of respondents. However auxiliary information available for respondents and nonrespondents is required to compute weights. In this paper statistical simulations are used to test the potential of aggregate data to correct nonresponse bias. This research compares individual data adjustments to the use of auxiliary aggregate data. The results show the use of aggregate data can improve survey representativity if three requirements are met: 1) the dependent variable is grouped, 2) the dependent and auxiliary variables are correlated and 3) the auxiliary variable is correlated with response propensities.

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Yadav, S. K., O. P. Yadav, and D. K. Yadav. "Dexterous Estimation of Population Mean in Survey Sampling Under Non-Response Error." International Journal of Mathematical, Engineering and Management Sciences 4, no. 6 (2019): 1307–24. http://dx.doi.org/10.33889/ijmems.2019.4.6-103.

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In this scripture, we ponder the problem of efficient estimation of population mean of study variable utilizing information on highly correlated auxiliary variables under the presence of non-response on either of the variables. For this purpose, we suggest, an improved estimator under three different situations of non-response. Under the first situation, estimation of population mean is done with the problem of non-response on both the study and the auxiliary variables with the additional condition that the population means of the auxiliary variables are known. The second situation is to estimate the population mean of primary variable when the problem of non-response is only on the primary variable but the population means of the auxiliary variables are known while under the third situation estimation is performed with the problem of non-response on both the study and the auxiliary variables but population mean of one of the auxiliary variables is unknown. We study the sampling properties of the suggested estimator under above three different situations of non-response. We compare the proposed estimator with the competing estimators of population mean, under three different situations of non-response. The efficiency conditions are obtained for all three situations. A numerical study is also carried out to verify the efficiency conditions.

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Gupta, Ruchi, and Sangeeta Malik. "Evaluating New Estimators in Ranked Set Sampling Using Auxiliary Variable." International Journal of Science and Research (IJSR) 13, no. 8 (2024): 1494–97. http://dx.doi.org/10.21275/sr24824152543.

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Kanwai, M. E., O. E. Asiribo, and A. Isah. "Use of Auxiliary Variables and Asymptotically Optimum Estimators in Double Sampling." International Journal of Statistics and Probability 5, no. 3 (2016): 55. http://dx.doi.org/10.5539/ijsp.v5n3p55.

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This paper explore the need for exploiting auxiliary variables in sample survey and utilizing asymptotically optimum estimator in double sampling to increase the efficiency of estimators. The study proposed two types of estimators with two auxiliary variables for two phase sampling when there is no information about auxiliary variables at population level. The expressions for the Mean Squared Error (MSE) of the proposed estimators were derived to the first order of approximation. An empirical comparative approach of the minimum variances and percent relative efficiency were adopted to study the efficiency of the proposed and existing estimators. It was established that, the proposed estimators performed more efficiently than the mean per unit estimator and other previous estimators that don’t use auxiliary variable and that are not asymptotically optimum. Also, it was established that estimators that are asymptotically optimum that utilized single auxiliary variable are more efficient than those that are not asymptotically optimum with two auxiliary variables.

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Chutiman. "ADAPTIVE CLUSTER SAMPLING USING AUXILIARY VARIABLE." Journal of Mathematics and Statistics 9, no. 3 (2013): 249–55. http://dx.doi.org/10.3844/jmssp.2013.249.255.

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Feng, Shiyong, and Guohua Zou. "Sample rotation method with auxiliary variable." Communications in Statistics - Theory and Methods 26, no. 6 (1997): 1497–509. http://dx.doi.org/10.1080/03610929708831996.

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Wang, Ting, Xiaofei Wang, Haibo Zhou, Jianwen Cai, and Stephen L. George. "Auxiliary variable-enriched biomarker-stratified design." Statistics in Medicine 37, no. 30 (2018): 4610–35. http://dx.doi.org/10.1002/sim.7938.

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Chhalotre, Rakesh, B. Samuel Naik, V. C. Karthik, et al. "Evaluating Model-assisted Estimators: A Comparative Study in High-dimensional Survey Data." Journal of Scientific Research and Reports 30, no. 9 (2024): 707–18. http://dx.doi.org/10.9734/jsrr/2024/v30i92398.

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Model-assisted estimators have gained significant attention due to their ability to efficiently utilize auxiliary information during the estimation process. These estimators rely on a working model that links the survey variable to the auxiliary variables, which is then fitted to the sample data to generate predictions. These predictions are subsequently integrated into the estimation procedures. In this study, were explores various model-assisted estimators including Generalized Regression (GREG), Ridge regression, Lasso regression, CART (Classification and Regression Tree), Random Forest, Cubist and Principal Components Regression (PCR) estimator. The analysis involved 2,000 samples of size 50 (n/N ≈ 10%) and employed a stepwise variable selection method to determine the most significant auxiliary variables, incrementally adding them to the model. The performance of these estimators was assessed using relative bias (RB), relative root mean square error (RRMSE) and relative efficiency (RE). Our findings reveal that tree-based models like CART and Random Forest and penalized regression estimators such as Ridge and Lasso display robustness with increased number of auxiliary variables. Among all the estimators, Random Forest consistently yielded the lowest RRMSE, particularly with five auxiliary variables, demonstrating superior efficiency. Conversely, the GREG estimator exhibited poor performance as the number of auxiliary variables increased. This study underscores the importance of selecting suitable model-assisted estimation procedures tailored to the data characteristics and the relationship between survey and auxiliary variables within this high-dimensional dataset.

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Erciulescu, Andreea L., and Wayne A. Fuller. "Small area prediction under alternative model specifications." Statistics in Transition new series 17, no. 1 (2016): 9–24. http://dx.doi.org/10.59170/stattrans-2016-001.

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Construction of small area predictors and estimation of the prediction mean squared error, given different types of auxiliary information are illustrated for a unit level model. Of interest are situations where the mean and variance of an auxiliary variable are subject to estimation error. Fixed and random specifications for the auxiliary variables are considered. The efficiency gains associated with the random specification for the auxiliary variable measured with error are demonstrated. A parametric bootstrap procedure is proposed for the mean squared error of the predictor based on a logit model. The proposed bootstrap procedure has smaller bootstrap error than a classical double bootstrap procedure with the same number of samples.

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Martínez, Sergio, María Dolores Illescas, Helena Martínez, and Antonio Arcos. "Calibration estimator for Head Count Index." International Journal of Computer Mathematics 97, no. 1-2 (2018): 51–62. https://doi.org/10.5281/zenodo.10582682.

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This paper considers the problem of estimating a poverty measure, the Head Count Index, using the auxiliary information available, which is incorporated into the estimationprocedure by calibration techniques. The proposed method does not directly use the auxiliary information provided by auxiliary variables related to the variable of interest in the calibration process, but the auxiliary information, after a transformation, is incorporated by calibration techniques applied to the distribution function of the study variable. Monte Carlo experiments were carried out for simulated data and for real data taken from the Spanish living conditions survey to explore the performance of the new estimation methods of the Head Count Index.

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Yu, Jianqi. "Inferences on A Normal Mean with an Auxiliary Variable." Journal of Statistics: Advances in Theory and Applications 25, no. 2 (2021): 51–59. http://dx.doi.org/10.18642/jsata_7100122198.

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Inferential procedures for a normal mean with an auxiliary variable are developed. First, the maximum likelihood estimation of the mean and its distribution are derived. Second, an F statistic based on the maximum likelihood estimation is proposed, and the hypothesis testing and confidence estimation are outlined. Finally, to illustrate the advantage of using auxiliary variable, Monte Carlo simulations are performed. The results indicate that using auxiliary variable can improve the efficiency of inference.

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Alghamdi, Abdulaziz S., and Hleil Alrweili. "A Comparative Study of New Ratio-Type Family of Estimators Under Stratified Two-Phase Sampling." Mathematics 13, no. 3 (2025): 327. https://doi.org/10.3390/math13030327.

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Two-phase sampling is a useful technique for sample surveys, particularly when prior auxiliary data is not accessible. The ranks of the auxiliary variable often coincide with those of the research variable when two variables are correlated. By considering this relationship, we can significantly increase estimator accuracy. In this paper, we use the ranks of the auxiliary variable along with extreme values to estimate the population mean of the study variable. Up to a first-order approximation, we analyze the characteristics of the suggested class of estimators with an emphasis on biases and mean squared errors in stratified two-phase sampling. The theoretical results are verified using different datasets and a simulation study, which demonstrates that the proposed estimators outperform the existing ones in terms of percent relative efficiency.

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Cathryn Donohue. "On variable auxiliary selection in Western Europe." Linguistic Research 32, no. 2 (2015): 469–80. http://dx.doi.org/10.17250/khisli.32.2.201508.008.

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Karna, Jaishree Prabha, and Dilip C. Nath. "Rotation Sampling Scheme Using Transformed Auxiliary Variable." Journal of Statistics and Management Systems 19, no. 6 (2016): 739–54. http://dx.doi.org/10.1080/09720510.2016.1190577.

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Sanusi, Ridwan A., Mu'azu Ramat Abujiya, Muhammad Riaz, and Nasir Abbas. "Combined Shewhart CUSUM charts using auxiliary variable." Computers & Industrial Engineering 105 (March 2017): 329–37. http://dx.doi.org/10.1016/j.cie.2017.01.018.

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Latifah, Leli, Kusman Sadik, and Indahwati Indahwati. "SIMULATION STUDY OF HIERARCHICAL BAYESIAN APPROACH FOR SMALL AREA ESTIMATION WITH MEASUREMENT ERROR." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 4 (2023): 2059–70. http://dx.doi.org/10.30598/barekengvol17iss4pp2059-2070.

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In small area estimation (SAE), the auxiliary variables used are commonly derived from registration data such as census and administrative data. It is assumed that the auxiliary variables are available for all areas. The limited availability of auxiliary variables can be an obstacle in SAE. The additional information from the survey can be alternative data, but it is assumed that the auxiliary variables will contain measurement errors. This study conducted a simulation of data that aims to handle when auxiliary variables are measured with errors. Two simulations were studied with some scenarios to the percentage area where the auxiliary variable is measured with error and scenarios to the generated auxiliary variables. Compare four methods: direct estimation, Fay-Herriot Empirical Best Linear Unbiased Prediction (EBLUP-FH), Ybarra-Lohr SAE with measurement error (SaeME), and Hierarchical Bayesian SaeME. The results show that, in both the simulation study, the Hierarchical Bayesian SaeME method gives a smaller the EMSE value than the other two methods when auxiliary information is measured with error.

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Alghamdi, Abdulaziz S., and Fatimah A. Almulhim. "Optimizing Finite Population Mean Estimation Using Simulation and Empirical Data." Mathematics 13, no. 10 (2025): 1635. https://doi.org/10.3390/math13101635.

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Two-phase sampling is an effective sampling approach that is useful in sample surveys when prior auxiliary information is not available. When two variables have an association, the ranks of the auxiliary variable are proportional to the study variable. Therefore, we can use these rankings to improve the accuracy of the estimators. In this article, we estimate the overall mean of the study variable based on extreme values and the ranks of the auxiliary variable. The properties of the proposed estimators with respect to biases and mean squared errors (MSEs) in two-phase sampling are obtained up to first order approximation. We verify the theoretical results and assess the performance of the proposed estimators using three datasets and a simulation study, which show that the proposed estimators outperform other existing estimators in terms of percent relative efficiency (PRE).

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Ahmad, Sohaib, Sardar Hussain, Erum Zahid, et al. "A Simulation Study: Population Distribution Function Estimation Using Dual Auxiliary Information under Stratified Sampling Scheme." Mathematical Problems in Engineering 2022 (October 5, 2022): 1–13. http://dx.doi.org/10.1155/2022/3263022.

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In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information, due to its usefulness in estimation methods. In this article, our main objective is to discover the problem associated with estimation of the finite population distribution function, using the known auxiliary variable, which occurs as the sample distribution function and the rank of the auxiliary variable. A new family of the finite population distribution function estimators is proposed in the stratified sampling scheme. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator, along with the eﬃciency conditions. Besides theoretical eﬃciency comparison, an empirical study has also been conducted to analyze the performance of estimators. A simulation study is also performed to observe the efficiency of the proposed estimators. The implementation of the proposed sampling scheme is illustrated by a practical example.

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Asghar, Amber, Aamir Sanaullah, Muhammad Hanif, and Laila A. Al-Essa. "Enhancing Precision in Population Variance Vector Estimation: A Two-Phase Sampling Approach with Multi-Auxiliary Information." Sains Malaysiana 53, no. 7 (2024): 1693–702. http://dx.doi.org/10.17576/jsm-2024-5307-16.

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To enhance precision in estimating unknown population parameters, an auxiliary variable is often used. However, in scenarios where required information on an auxiliary variable is partially or fully unavailable, two-phase sampling is commonly employed. The challenge of estimating the variance vector using multi-auxiliary variables is a less explored area in current literature. This paper addresses the estimation of vector of unknown population variances for multiple study variables by using an estimated vector of variances derived from multi-auxiliary information. This approach is particularly relevant when population variances for the multi-auxiliary variables are not known prior to the survey. The paper introduces a generalized variance and a vector of biases for the proposed multivariate estimator. Special cases of the proposed multivariate variance estimator are provided, accompanied by expressions for mean square errors. Theoretical mathematical conditions are discussed to guide the preference for the proposed estimator. Through the analysis of real-world application-based data, the applicability and efficiency of the proposed multivariate variance estimator are demonstrated, outperforming modified versions of multivariate variance estimators. Additionally, a simulation study validates the superior performance of the proposed estimator compared to its modified estimators.

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Hussain, Sardar, Sohaib Ahmad, Sohail Akhtar, Amara Javed, and Uzma Yasmeen. "Estimation of finite population distribution function with dual use of auxiliary information under non-response." PLOS ONE 15, no. 12 (2020): e0243584. http://dx.doi.org/10.1371/journal.pone.0243584.

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In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.

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Hoxha, Besim. "Two-phased inventory of standing volume in mountain forests with the use of aerial photographs." Folia Forestalia, Series A - Forestry 54(2) (July 1, 2012): 123–33. https://doi.org/10.5281/zenodo.30736.

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This study aimed to elaborate and develop the existing methods used in inventorying lowland forest and adapt them for mountainous forests. The inventory of mountain forests with the use of CIR aerial photographs in this study relied on the implementation of the 3D (three-dimensional) methods and it was characterised by two phases. In the 1st p hase the auxiliary variables (e.g. crown cover, height of dominant trees, density) were measured on the aerial photographs (355 circular plots). Variable of interest (standing volume) was recorded during the terrestrial survey on the corresponding ground sample plots. A statistical relationship was established between the variable of interest and the auxiliary variables by means of multiple regressions. In the 2nd phase selected auxiliary variables were measured on the enlarged set of 2772 plots on the aerial photographs only. The variable of interest (standing volume) was computed for the whole forest area by using the regression model developed in the 1st phase and t he aid of the variables measured in the 2nd phase.

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Imori, Shinpei, and Hidetoshi Shimodaira. "An Information Criterion for Auxiliary Variable Selection in Incomplete Data Analysis." Entropy 21, no. 3 (2019): 281. http://dx.doi.org/10.3390/e21030281.

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Statistical inference is considered for variables of interest, called primary variables, when auxiliary variables are observed along with the primary variables. We consider the setting of incomplete data analysis, where some primary variables are not observed. Utilizing a parametric model of joint distribution of primary and auxiliary variables, it is possible to improve the estimation of parametric model for the primary variables when the auxiliary variables are closely related to the primary variables. However, the estimation accuracy reduces when the auxiliary variables are irrelevant to the primary variables. For selecting useful auxiliary variables, we formulate the problem as model selection, and propose an information criterion for predicting primary variables by leveraging auxiliary variables. The proposed information criterion is an asymptotically unbiased estimator of the Kullback–Leibler divergence for complete data of primary variables under some reasonable conditions. We also clarify an asymptotic equivalence between the proposed information criterion and a variant of leave-one-out cross validation. Performance of our method is demonstrated via a simulation study and a real data example.

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Feriyanto, Muhamad, Arie Wahyu Wijayanto, Ika Yuni Wulansari, and Novia Budi Parwanto. "Small Area Estimation Approaches Using Satellite Imageries Auxiliary Data for Estimating Per Capita Expenditure in West Java, Indonesia." Jurnal Aplikasi Statistika & Komputasi Statistik 16, no. 2 (2024): 205–21. https://doi.org/10.34123/jurnalasks.v16i2.799.

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Introduction/Main Objectives: The economy of a country can determine the welfare of its people. One of the economic indicators in Indonesia is per capita expenditure, which has the lowest estimation at the district level. Background Problems: Sub-district level estimates provide detailed information on inequality that cannot be explained at the district level. Unfortunately, subdistrict level estimates of per capita expenditure in Indonesia have poor Relative Standard Error (RSE) values. Research Method: The Small Area Estimation (SAE) method can improve estimator accuracy on small samples by using auxiliary variable information. Novelty: The existence of big geospatial data such as remote sensing provides an advantage in the efficient use of auxiliary variables. Finding Result: The Empirical Best Linear Unbiased Prediction (EBLUP) model using Nighttime Light Intensity (NTL) as an auxiliary variable provides the best results of the five proposed models. Remote sensing data can potentially be used in SAE auxiliary variables. It provides opportunities for cheaper, faster, and more efficient data collection compared to conventional data.

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Danish, Faizan, Rafia Jan, Muhammad Daniyal, and Kassim Tawiah. "Optimum Stratification Using Dynamic Programming with a Mixture of Ratio and Product Estimators under Super Population Model." Mathematical Problems in Engineering 2023 (April 29, 2023): 1–10. http://dx.doi.org/10.1155/2023/3149912.

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In this study, we have utilized two study variables and one auxiliary variable. The auxiliary variable is used as the stratification variable, and we selected the sample using the stratification variable with a mixture of ratio and product estimators. Under super population set-up, minimal equations have been obtained through minimization of the aggregated variance with the help of the variables under study. The objective function is minimized with respect to the constraints under consideration. The dynamic programming approach has been used to minimize the variance and obtain the optimum strata boundaries. Empirical studies have also been made on the proposed rule utilizing different distributions. A simulation study has been done which shows the gain in precision using the proposed method.

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Ali, Asad, Muhammad Moeen Butt, and Muhammad Zubair. "Generalized Chain Regression-cum-Chain Ratio Estimator for Population Mean under Stratified Extreme-cum-Median Ranked Set Sampling." Mathematical Problems in Engineering 2022 (January 4, 2022): 1–13. http://dx.doi.org/10.1155/2022/9556587.

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Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under ranked set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized chain regression-cum-chain ratio type estimator to estimate finite population mean of study variable under stratified extreme-cum-median ranked set sampling utilizing information on two auxiliary variables. Mean square error (MSE) of the proposed generalized estimator is derived up to first order of approximation. The applications of the proposed estimator under symmetrical and asymmetrical probability distributions are discussed using simulation study and real-life data set for comparisons of efficiency. It is concluded that the proposed generalized estimator performs efficiently as compared to some existing estimators. It is also observed that the efficiency of the proposed estimator is directly proportional to the correlations between the study variable and its auxiliary variables.

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Çetin, Arzu, and Nursel Koyuncu. "Calibration estimator of population mean in stratified extreme ranked set sampling with simulation study." Filomat 38, no. 2 (2024): 599–608. http://dx.doi.org/10.2298/fil2402599c.

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Calibration estimation sets the original weights to include the known population characteristics of auxiliary variables using constraints. In this article, we have proposed a new calibration estimator of the population mean in stratified extreme ranked set sampling design, which is more efficient and costeffective design against other sampling designs in the literature. A detailed simulation study is carried out to observe the performance of proposed estimators. We have used the information of auxiliary variable to avoid ranking errors in our simulations. We have created samples from a bi-variate normal distribution with different values of ?xy. While one of these variables is taken as the variable of interest, the other is accepted as an auxiliary variable and used in ranking the sample units in each set. As a result of the simulation study using both synthetic and real data sets, we have found that our proposed estimators are more efficient than Sinha et al. [19] calibration estimator and classical stratified estimator.

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Su, Ying Ying, Xing Hua Liu, Jing Zhe Li, Tai Fu Li, and Ke Sheng Yan. "The Soft Sensing of Battery Capacity Based on RReliefF Algorithm and Neural Network." Advanced Materials Research 765-767 (September 2013): 809–12. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.809.

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To solve the problem of too many variable numbers which makes the model complex, a kind of auxiliary variables selection method is established. After that, soft sensing of lead-acid battery capacity is put forward. First, the RReliefF method is adopted to define quantitatively the influence of auxiliary variables. Then, the soft sensing model is built up with all the combination of auxiliary variables with BP neural network. Simulation results show that the soft sensing of battery capacity is established ideal. It provides theoretical feasibility to omit the battery discharge capacity in the process of production inspection process.

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Al-Jararha, Jehad, and Ala' Bataineh. "Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study." Austrian Journal of Statistics 44, no. 1 (2014): 33–46. http://dx.doi.org/10.17713/ajs.v44i1.15.

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The estimation of the population total $t_y,$ by using one or moreauxiliary variables, and the population ratio $\theta_{xy}=t_y/t_x,$$t_x$ is the population total for the auxiliary variable $X$, for afinite population are heavily discussed in the literature. In thispaper, the idea of estimation the finite population ratio$\theta_{xy}$ is extended to use the availability of auxiliaryvariable $Z$ in the study, such auxiliary variable is not used inthe definition of the population ratio. This idea may be supported by the fact that the variable $Z$ is highly correlated with the interest variable $Y$ than the correlation between the variables $X$ and $Y.$ The availability of such auxiliary variable can be used to improve the precision of the estimation of the population ratio. To our knowledge, this idea is not discussed in the literature. The bias, variance and the mean squares error are given for our approach. Simulation from real data set, the empirical relative bias and the empirical relative mean squares error are computed for our approach and different estimators proposed in the literature for estimating the population ratio $\theta_{xy}.$ Analytically and the simulation results show that, by suitable choices, our approach gives negligible bias and has less mean squares error.

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Basak, Pradip, Kaustav Aditya, and Deepak Singh. "Calibration Estimation of Population Total in Two-Stage Sampling Design under unavailability of Population Level Auxiliary Information for the selected PSUs." Journal of the Indian Society of Agricultural Statistics 78, no. 1 (2024): 29–35. http://dx.doi.org/10.56093/jisas.v78i1.4.

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Calibration approach is a popular technique in sample surveys which incorporates auxiliary information in the estimation process assuming that population aggregates of auxiliary variable are available. Many often under two-stage sampling design, such population aggregates of auxiliary variable, i.e., population mean or total are unavailable and under such situations, estimation of population total has been limited to the use of two phase sampling. Therefore, in the present study, efficient estimator of population total is developed under two-stage sampling design when population aggregates of auxiliary variable are unavailable for the selected psu’s. The calibrated estimator is developed using the information on known population aggregates of additional auxiliary variable which is less linearly related to the study variable through two step calibration approach. The approximate variance and variance estimator of the proposed calibrated estimator has also been developed. Empirical evaluations using both real and simulated data shows the superior performance of the developed calibrated estimator in comparison to the existing estimators.

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Chen, Jen-Hsiang, and Shin-Li Lu. "Economic-Statistical Performance of Auxiliary Information-Based Maximum EWMA Charts for Monitoring Manufacturing Processes." Mathematics 10, no. 13 (2022): 2320. http://dx.doi.org/10.3390/math10132320.

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An auxiliary information-based maximum exponentially weighted moving average chart, namely, the AIB-MaxEWMA chart, is superior to the existing MaxEWMA chart in detecting small process mean and/or variability shifts. To date, AIB-MaxEWMA chart was designed based on the statistical perspective, which ignores the cost of process monitoring. The economic-statistical performance of the AIB-MaxEWMA chart for monitoring process shifts is investigated. The Monte Carlo simulation was conducted to determine the optimal decision variables, such as sample size, sampling interval, control limit constant, and smoothing constant, by minimizing the expected cost function under the statistical constraints. Numerical simulations indicate that when an auxiliary variable is highly related to the study variable, AIB-MaxEWMA charts not only have better statistical performance, but also have lower expected costs than MaxEWMA charts. Sensitivity analyses also show that a larger expected time to sample an auxiliary variable results in larger optimal expected costs and lower optimal sample size and sampling interval. The relationship between optimal decision variables and minimal costs is valuable for reference by researchers or process engineers.

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Liu, Zhifan, Chunling Liu, and Zhihua Sun. "Consistent model check of errors-in-variables varying-coefficient model with auxiliary variable." Journal of Statistical Planning and Inference 198 (January 2019): 13–28. http://dx.doi.org/10.1016/j.jspi.2018.03.002.

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Subramani, J., and G. Kumarapandiyan. "Variance Estimation Using Median of the Auxiliary Variable." International Journal of Probability and Statistics 1, no. 3 (2012): 36–40. http://dx.doi.org/10.5923/j.ijps.20120103.02.

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Al-Jararha, J., and Mazen Sulaiman. "Horvitz-Thompson estimator based on the auxiliary variable." Statistics in Transition New Series 21, no. 1 (2020): 37–53. http://dx.doi.org/10.21307/stattrans-2020-003.

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Martell, Craig A., and John A. Lawton. "Adjoint variable solutions via an auxiliary optimization problem." Journal of Guidance, Control, and Dynamics 18, no. 6 (1995): 1267–72. http://dx.doi.org/10.2514/3.21540.

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Brown, Kate, Dinesh K. Sharma, and S. K. Yadav. "Estimating Peppermint Oil Yields with Auxiliary Variable Information." International Journal of Operational Research 1, no. 1 (2021): 1. http://dx.doi.org/10.1504/ijor.2021.10025383.

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Naz, Farah, Tahir Nawaz, Tianxiao Pang, and Muhammad Abid. "Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers." Symmetry 12, no. 1 (2019): 16. http://dx.doi.org/10.3390/sym12010016.

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The use of auxiliary information in survey sampling to enhance the efficiency of the estimators of population parameters is a common phenomenon. Generally, the ratio and regression estimators are developed by using the known information on conventional parameters of the auxiliary variables, such as variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis, or correlation between the study and auxiliary variable. The efficiency of these estimators is dubious in the presence of outliers in the data and a nonsymmetrical population. This study presents improved variance estimators under simple random sampling without replacement with the assumption that the information on some nonconventional dispersion measures of the auxiliary variable is readily available. These auxiliary variables can be the inter-decile range, sample inter-quartile range, probability-weighted moment estimator, Gini mean difference estimator, Downton’s estimator, median absolute deviation from the median, and so forth. The algebraic expressions for the bias and mean square error of the proposed estimators are obtained and the efficiency conditions are derived to compare with the existing estimators. The percentage relative efficiencies are used to numerically compare the results of the proposed estimators with the existing estimators by using real datasets, indicating the supremacy of the suggested estimators.

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Sadinle, Mauricio, and Jerome P. Reiter. "Sequentially additive nonignorable missing data modelling using auxiliary marginal information." Biometrika 106, no. 4 (2019): 889–911. http://dx.doi.org/10.1093/biomet/asz054.

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Summary We study a class of missingness mechanisms, referred to as sequentially additive nonignorable, for modelling multivariate data with item nonresponse. These mechanisms explicitly allow the probability of nonresponse for each variable to depend on the value of that variable, thereby representing nonignorable missingness mechanisms. These missing data models are identified by making use of auxiliary information on marginal distributions, such as marginal probabilities for multivariate categorical variables or moments for numeric variables. We prove identification results and illustrate the use of these mechanisms in an application.

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Xu, Ming, Xiao-meng Wu, Xin Yu, and Guo-jin Chen. "Dynamic performance of auxiliary hydraulic power unit based electro-hydraulic variable speed drive system." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 16 (2017): 2926–36. http://dx.doi.org/10.1177/0954406217727770.

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Inability of dynamic performances, especially the acceleration response, strongly inhibits the application of electro-hydraulic variable speed drive, even though its intrinsic energy-saving potential. In contrast to variable speed drive, the valve-controlled actuator system shows the capacity of fast response and accurate control precision, but it consumes more energy. The controllable auxiliary power unit based electro-hydraulic variable speed drive system is probably a solution to enhance dynamic performance of variable speed drive on the basis of energy-saving. Except for the principal variable speed power source, there is an auxiliary power source—auxiliary power unit, which is actually a semi-active hydraulic accumulator unit. The auxiliary power unit can detect the relation between the supplied power by power source and the demanded power by actuator, and then release or absorb hydraulic power to improve actuator dynamic response. The dynamic performance of auxiliary power unit based variable speed drive system was investigated experimentally. Firstly, the set-up of proposed drive system was introduced. Dedicated to the complicated characteristics of multi-input-multi-output and strongly nonlinearity, the mathematical model was deduced, and a hierarchical control strategy was illustrated. The experimental results under two typical variable-load conditions were discussed. Furthermore, the comparisons were explained with the other three drive systems, which were valve-controlled motor drive, conventional variable speed drive, and pump-valve compound drive. Based on the experimental results, it is concluded that the auxiliary power unit based variable speed drive demonstrates an excellent dynamic performance, which can significantly improve the actuator response and control precision, as well as obtain a good energy-saving behavior.

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Dahwan Aziz, Sheerin, and Azka Ubaidillah. "Big Data for Small Area Estimation: Happiness Index with Twitter Data." Proceedings of The International Conference on Data Science and Official Statistics 2021, no. 1 (2022): 963–72. http://dx.doi.org/10.34123/icdsos.v2021i1.248.

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Data availability for small area level is one of the keys to the success of regional development. However, direct estimation of small areas can produce high error due to inadequate sample sizes so the estimation is not reliable. One of alternative solution to this problem is to use the Small Area Estimation (SAE) method which can improve precision by "borrows strength" of the corresponding region information or auxiliary variable information that is strongly related to the response variable. This study uses two SAE models, namely SAE EBLUP Fay-Herriot model with auxiliary variables Podes data and SAE with Error Measurement with auxiliary variable Twitter data. Estimation results using the SAE method are better than direct estimates. This is shown by the RSE value which produced from SAE method, both the EBLUP model and Measurement Error, is smaller than the direct estimate. Therefore, big data can be used as an alternative variable in the SAE model because the data is available in real-time, covers up to the smallest area, and relatively low cost.

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Li, Longhao, and Yongshou Dai. "An adaptive soft sensor deterioration evaluation and model updating method for time-varying chemical processes." Chemical Industry and Chemical Engineering Quarterly 26, no. 2 (2020): 135–49. http://dx.doi.org/10.2298/ciceq190419032l.

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Due to the time-varying nature of chemical processes, soft sensor models deteriorate, and data prediction accuracy decreases. To address this problem, an adaptive soft sensor modeling method is proposed that not only evaluates the model deterioration by an adaptive moving window-constrained statistical hypothesis test, but also adaptively updates the modeling samples using moving window-cosine similarity. First, this method evaluates the model deterioration via positioning by constrained statistical hypothesis testing based on the differences between the prediction performance evaluation index data obtained from moving window stepping and the original prediction performance evaluation indexes. Additionally, the dynamic temporal variation in chemical processes causes changes in the impacts of the auxiliary variables on the dominant variable, and this effect limits the improvement in the prediction accuracy of the soft sensor model by updating only the auxiliary variable data. The moving window-cosine similarity method is combined to propose a strategy that updates both the modeled auxiliary variables and the auxiliary variable data. Finally, the parameters of the soft sensor model are optimized via particle swarm optimization (PSO) to improve the fitting performance. Simulated data of a continuous stirred tank reactor (CSTR) and actual data from a debutanizer column process (DCP) are used for model verification to evaluate the performance of the proposed adaptive soft sensor modeling method, and the results show its effectiveness.

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Zhao, Zebin, Rui Jin, Jian Kang, Chunfeng Ma, and Weizhen Wang. "Using of Remote Sensing-Based Auxiliary Variables for Soil Moisture Scaling and Mapping." Remote Sensing 14, no. 14 (2022): 3373. http://dx.doi.org/10.3390/rs14143373.

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Soil moisture is one of the core hydrological and climate variables that crucially influences water and energy budgets. The spatial resolution of available soil moisture products is generally coarser than 25 km, which limits their hydro-meteorological and eco-hydrological applications and the management of water resources at watershed and agricultural scales. A feasible solution to overcome these limitations is to downscale coarse soil moisture products with the support of higher-resolution spatial information. Although many auxiliary variables have been used for this purpose, few studies have analyzed their applicability and effectiveness in arid regions. To this end, we comprehensively evaluated four commonly used auxiliary variables, including NDVI (Normalized Difference Vegetation Index), LST (Land Surface Temperature), TVDI (Temperature Vegetation Dryness Index), and SEE (Soil Evaporative Efficiency), against ground-based soil moisture observations during the vegetation growing season in the Heihe River Basin, China. Performance metrics indicated that SEE is most sensitive (R2 ≥ 0.67) to soil moisture because it is controlled by soil evaporation limited by the available soil moisture. The similarity of spatial patterns also showed that SEE best captures soil moisture changes, with the STD (standard deviation) of the HD (Hausdorff Distance) less than 0.058 when compared with PLMR (Polarimetric L-band Multi-beam Radiometer) soil moisture products. In addition, soil moisture was mapped by RF (Random Forests) using both single auxiliary variables and 11 types of multiple auxiliary variable combinations. SEE was found to be the best auxiliary variable for scaling and mapping soil moisture with accuracy of 0.035 cm3/cm3. Among the multiple auxiliary variables, the combination of LST, NDVI, and SEE was found to best enhance the scaling and mapping accuracy of soil moisture with 0.034 cm3/cm3.

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Elkasabi, Mahmoud A., Steven G. Heeringa, and James M. Lepkowski. "Joint Calibration Estimator for dual frame surveys." Statistics in Transition new series 16, no. 1 (2015): 7–36. http://dx.doi.org/10.59170/stattrans-2015-001.

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Many dual frame estimators have been proposed in the statistics literature. Some of these estimators are theoretically optimal but hard to apply in practice, whereas others are applicable but have larger variances than the first group. In this paper, a Joint Calibration Estimator (JCE) is proposed that is simple to apply in practice and meets many desirable properties for dual frame estimators. The JCE is asymptotically design unbiased conditional on the strong relationship between the estimation variable and the auxiliary variables employed in the calibration. The JCE achieves better performance when the auxiliary variables can fully explain the variability in the study variables or at least when the auxiliary variables are strong correlates of the estimation variables. As opposed to the standard dual frame estimators, the JCE does not require domain membership information. Even if included in the JCE auxiliary variables, the effect of the randomly misclassified domains does not exceed the random measurement error effect. Therefore, the JCE tends to be robust for the misclassified domains if included in the auxiliary variables. Meanwhile, the misclassified domains can significantly affect the unbiasedness of the standard dual frame estimators as proved theoretically and empirically in this paper.

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Swain, A. K. P. C. "On classes of modified ratio type and regression-cum-ratio type estimators in sample surveys using two auxiliary variables." Statistics in Transition new series 13, no. 3 (2013): 473–94. http://dx.doi.org/10.59170/stattrans-2012-035.

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In this paper generalized classes of modified ratio type and regression-cum-ratio type estimators of the finite population mean of the study variable are suggested in the presence of two auxiliary variables in simple random sampling without replacement when the population means of the auxiliary variables are known in advance. Some special cases of the generalized estimators are compared with respect to their biases and efficiencies both theoretically and with the help of some natural populations.

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Mehta, Nitu, and V. L. Mandowara. "Some Efficient Methods to Remove Bias in Ratio and Product Types Estimators in Ranked Set Sampling." International Journal of Bio-resource and Stress Management 13, no. 3 (2022): 276–82. http://dx.doi.org/10.23910/1.2022.2771a.

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Ranked set sampling is one method to potentially increase precision and reduce costs by using quantitative or qualitative information to obtain a more representative sample. Use of auxiliary information has shown its significance in improvement of efficiency of estimators of unknown population parameters. Ratio estimator is used when auxiliary information in the form of population mean of auxiliary variable at estimation stage for the estimation of population parameters when study and auxiliary variable are positively correlated. In case of negative correlation between study variable and auxiliary variable, Product estimator is defined for the estimation of population mean. This paper proposed the problem of reducing the bias of the ratio and product estimators of the population mean in ranked set sampling (RSS). This paper suggested several type unbiased estimators of the finite population mean using information on known population parameters of the auxiliary variable in ranked set sampling. An important objective in any statistical estimation procedure is to obtain the estimators of parameters of interest with more precision. The Variance of the proposed unbiased ratio and product estimators are obtained up to first degree of approximation. Theoretically, it is shown that these suggested estimators are more efficient than the unbiased estimators in Simple random sampling. A numerical illustration is also carried out to demonstrate the merits of the proposed estimators using RSS over the usual estimators in SRS.

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Xu, Zihang, and Balgobin Nandram. "Supplementing a Non-probability Sample With a Probability Sample to Predict the Finite Population Mean." International Journal of Statistics and Probability 13, no. 2 (2024): 16. http://dx.doi.org/10.5539/ijsp.v13n2p16.

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We show how to analyze a non-probability sample (nps) with limited information from a small probability sample (ps). The most practical case is when the nps has auxiliary variables and study variable but no survey weights and the ps has&nbsp; known weights, auxiliary variables, but no study variable. Two samples are taken from the same population and the variables are common to both the nps and the ps. A large non-probability sample can reduce the cost but will give biased estimator with small variance, the small probability sample can provide supplemental information. Following this, we apply these weights to fit a mixture model, enhancing the robustness of the results and enabling the estimation of the finite population mean. Additionally, we present a method to enhance the efficiency of the Gibbs sampler.

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Djulaikah, Siti. "ERROR ANALYSIS ON THE AUXILIARY VERBS MADE BY THE TENTH GRADERS OF MAN 2 SAMARINDA." LINGUA: Journal of Language, Literature and Teaching 13, no. 1 (2016): 103. http://dx.doi.org/10.30957/lingua.v13i1.16.

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This study used qualitative design focusing on the errors made by the second year students of MAN 2 Samarinda. The variable of this study was errors on auxiliary verbs. The variable was measured by using an objective test on auxiliary verbs. The instrument of the study was a test on auxiliary verbs. The data were analyzed the kinds of typical errors which are classified into four, they are: omission, addition, misformation, misordering errors. The components of auxiliary verbs test were: to do (do, does, did), to have (have, has), and modal auxiliary (can, could, will, would, may, and must). The study discovered that kinds of typical errors on auxiliary verbs are classified into four kinds of typical errors: omission errors, addition errors (double marking and regularization), misformation errors and miscellaneous errors. The typical errors present on auxiliary verbs are classified into four kinds of typical errors: (1) to do, including: errors in adding “do”, “does” and “did”, misuse in using “do”, “does” and “did”. (2) to have including: errors in adding “have” and “has”, double in marking auxiliary verbs, in this case to be and to have, (3) modal auxiliary including: false in choosing the right modal auxiliary.

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Castrignanò, Annamaria, Gabriele Buttafuoco, Massimo Conforti, Mauro Maesano, Federico Valerio Moresi, and Giuseppe Scarascia Mugnozza. "Improving the Spatial Prediction of Sand Content in Forest Soils Using a Multivariate Geostatistical Analysis of LiDAR and Hyperspectral Data." Remote Sensing 15, no. 18 (2023): 4416. http://dx.doi.org/10.3390/rs15184416.

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Soil sand particles play a crucial role in soil erosion because they are more susceptible to being detached and transported by erosive forces than silt and clay particles. Therefore, in soil erosion assessment and mitigation, it is crucial to model and predict soil sand particles at unsampled locations using appropriate methods. The study was aimed to evaluate the ability of a multivariate approach based on non-stationary geostatistics to merge LiDAR and visible-near infrared (Vis-NIR) diffuse reflectance data with laboratory analyses to produce high-resolution maps of soil sand content. Remotely sensed, high-resolution LiDAR-derived topographic attributes can be used as auxiliary variables to estimate soil textural particle-size fractions. The proposed approach was compared with the commonly used univariate approach of ordinary kriging to evaluate the contribution of auxiliary variables. Soil samples (0–0.20 m depth) were collected at 135 locations within a 139 ha forest catchment with granitic parent material and subordinately alluvial deposits, where soils classified as Typic Xerumbrepts and Ultic Haploxeralf crop out. A number of linear trend models coupled with different auxiliary variables were compared. The best model for predicting sand content was the one with elevation derived from LIDAR data as the only auxiliary variable. Although the improvement in estimation over the univariate model was rather marginal, the proposed approach proved very flexible and scalable to include any type of auxiliary variable. The application of LiDAR data is expected to expand as it allows the high-resolution prediction of soil properties, generally insufficiently sampled, at different spatial scales.

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Skinner, Chris, and Nuanpan Lawson. "Nonresponse Adjustment using Auxiliary Variables Subject themselves to Missing Data." WSEAS TRANSACTIONS ON SYSTEMS 24 (April 1, 2025): 106–11. https://doi.org/10.37394/23202.2025.24.12.

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Nonresponse is a significant matter that cannot be denied in a sample survey. Declining response rates lead to increasing nonresponse bias which affects the estimated bias. Nonresponse adjustment can be used to deal with unit nonresponse by using nonresponse weight. Two possible models in which missingness in an ancillary database may be correlated with missingness in a survey are considered in this study for estimating the population mean when nonresponse occurs on both the study and auxiliary variables. Two auxiliary variables where one auxiliary variable is fully observed and some part of the other is missing are considered in the possible models. Simulation studies are carried on to see how the nonresponse adjustment using auxiliary variables that subject themselves to nonresponse work under the possible models. The simulation results show that the weighted mean performed the best in removing the bias and gave the minimum mean square error compared to the unweighted mean which was affected by nonresponse.

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Hussain, Saddam, Mi Zichuan, Sardar Hussain, et al. "On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling." Journal of Probability and Statistics 2020 (September 26, 2020): 1–13. http://dx.doi.org/10.1155/2020/1693612.

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In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.

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