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Journal articles on the topic 'Horvitz-Thompson estimator'

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Published: 4 June 2021

Last updated: 8 September 2023

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1

Théberge, Alain. "Estimation when the Covariance Structure of the Variable of Interest is Positive Definite." Journal of Official Statistics 33, no. 1 (March 1, 2017): 275–99. http://dx.doi.org/10.1515/jos-2017-0014.

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Abstract Generalized regression (GREG) estimation uses a model that assumes that the values of the variable of interest are not correlated. An extension of the GREG estimator to the case where the vector of interest has a positive definite covariance structure is presented in this article. This extension can be translated to the calibration estimators. The key to this extension lies in a generalization of the Horvitz-Thompson estimator which, in some sense, also assumes that the values of the variable of interest are not correlated. The Godambe-Joshi lower bound is another result which assumes a model with no correlation. This is also generalized to a vector of interest with a positive definite covariance structure, and it is shown that the generalized calibration estimator asymptotically attains this generalized lower bound. Properties of the new estimators are given, and they are compared with the Horvitz-Thompson estimator and the usual calibration estimator. The new estimators are applied to the Canadian Reverse Record Check survey and to the problem of variance estimation.

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Biyani, S. H., and Chand K. Midha. "A Generalized Formula for Variance in Unequal Probability Sampling." Calcutta Statistical Association Bulletin 48, no. 3-4 (September 1998): 241–44. http://dx.doi.org/10.1177/0008068319980312.

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A variance formula is given for a general class of estimators for any fixed sample size design. A formula for an unbiased estimator of the variance is also provided. These results generalize the Yates-Grundy variance formula of the Horvitz-Thompson estimator.

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3

Zhu, Guangyu, and Liyong Fu. "k-step adaptive cluster sampling with Horvitz–Thompson estimator." International Journal of Biomathematics 11, no. 02 (February 2018): 1850029. http://dx.doi.org/10.1142/s1793524518500298.

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Adaptive cluster sampling (ACS) has been widely used for data collection of environment and natural resources. However, the randomness of its final sample size often impedes the use of this method. To control the final sample sizes, in this study, a [Formula: see text]-step ACS based on Horvitz–Thompson (HT) estimator was developed and an unbiased estimator was derived. The [Formula: see text]-step ACS-HT was assessed first using a simulated example and then using a real survey for numbers of plants for three species that were characterized by clustered and patchily spatial distributions. The effectiveness of this sampling design method was assessed in comparison with ACS Hansen–Hurwitz (ACS-HH) and ACS-HT estimators, and [Formula: see text]-step ACS-HT estimator. The effectiveness of using different [Formula: see text]-step sizes was also compared. The results showed that [Formula: see text]-step ACS-HT estimator was most effective and ACS-HH was the least. Moreover, stable sample mean and variance estimates could be obtained after a certain number of steps, but depending on plant species. [Formula: see text]-step ACS without replacement was slightly more effective than that with replacement. In [Formula: see text]-step ACS, the variance estimate of one-step ACS is much larger than other [Formula: see text]-step ACS ([Formula: see text]), but it is smaller than ACS. This implies that [Formula: see text]-step ACS is more effective than traditional ACS, besides, the final sample size can be controlled easily in population with big clusters.

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Magnussen, Steen, and Thomas Nord-Larsen. "A Jackknife Estimator of Variance for a Random Tessellated Stratified Sampling Design." Forest Science 65, no. 5 (March 12, 2019): 543–47. http://dx.doi.org/10.1093/forsci/fxy070.

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Abstract Semisystematic sampling designs—in which a population area frame is tessellated into cells, and a randomly located sample is taken from each cell—affords random tessellated stratified (RTS) Horvitz–Thompson-type estimators. Forest inventory applications with RTS estimators are rare, possibly because of computational complexities with the estimation of variance. To reduce this challenge, we propose a jackknife estimator of variance for RTS designs. We demonstrate an application with a model-assisted ratio of totals estimator and data from the Danish National Forest Inventory. RTS estimators of standard error were, as a rule, smaller than comparable estimates obtained under the assumption of simple random sampling. The proposed jackknife estimator performed well.

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Mohd Tajuddin, Razik Ridzuan, Noriszura Ismail, and Kamarulzaman Ibrahim. "On Variance Estimation for the Population Size Estimator under One-Inflated Positive Poisson Distribution." Malaysian Journal of Fundamental and Applied Sciences 18, no. 2 (May 16, 2022): 237–44. http://dx.doi.org/10.11113/mjfas.v18n2.2372.

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Let NO1PPbe the Horvitz-Thompson estimator for the population size with one-inflated positive Poisson distribution as the underlying distribution. We estimate the variance of this estimator using conditional expectation technique and provide some descriptions on the variance and its associated confidence interval based on simulation study and real data applications.

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6

Bakar, K. S. "Inference on Environmental Population Using Horvitz-Thompson Estimator." Journal of Environmental Informatics 16, no. 1 (September 2010): 27–34. http://dx.doi.org/10.3808/jei.201000175.

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7

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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8

Magnussen, Steen. "A Horvitz-Thompson-type estimator of species richness." Environmetrics 22, no. 7 (May 2, 2011): 901–10. http://dx.doi.org/10.1002/env.1117.

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9

Stoyan, Dietrich, Helga Stoyan, André Tscheschel, and Torsten Mattfeldt. "ON THE ESTIMATION OF DISTANCE DISTRIBUTION FUNCTIONS FOR POINT PROCESSES AND RANDOM SETS." Image Analysis & Stereology 20, no. 1 (May 3, 2011): 65. http://dx.doi.org/10.5566/ias.v20.p65-69.

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This paper discusses various estimators for the nearest neighbour distance distribution function D of a stationary point process and for the quadratic contact distribution function Hq of a stationary random closed set. It recommends the use of Hanisch's estimator of D, which is of Horvitz-Thompson type, and the minussampling estimator of Hq. This recommendation is based on simulations for Poisson processes and Boolean models.

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10

Sengupta, S. "A Comparison Between PPSWR and Brewer's ∏PSWOR Procedures." Calcutta Statistical Association Bulletin 35, no. 3-4 (September 1986): 207–10. http://dx.doi.org/10.1177/0008068319860311.

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It is proved that the variance of the Horvitz-Thompson estimator (HTE) of a finite population total based on Brewer's (1975) ∏PSWOR procedure is smaller than the variance or the Hansen-Hurwitz estimator (HHB) based on a PPSWR sample involvioa the same number of draws.

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11

Schoch, Tobias. "On the Strong Law of Large Numbers for Nonnegative Random Variables. With an Application in Survey Sampling." Austrian Journal of Statistics 50, no. 3 (July 5, 2021): 1–12. http://dx.doi.org/10.17713/ajs.v50i3.631.

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Strong laws of large numbers with arbitrary norming sequences for nonnegative not necessarily independent random variables are obtained. From these results we establish, among other things, stability results for weighted sums of nonnegative random variables. A survey sampling application is provided on strong consistency of the Horvitz--Thompson estimator and the ratio estimator.

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12

Ikughur, A. J., M. T. Imande, and S. Vambe. "Investigating the Performance of Horvitz-Thompson and Generalized Regression Estimators in Small Domains with Application to Income and Expenditure of Households in Makurdi-Nigeria." NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES 1 (December 30, 2019): 214–22. http://dx.doi.org/10.46912/napas.124.

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In this study, efficiencies of Horvitz-Thompson (HT) and Generalized Regression (GREG) estimatorsare investigated in small domains namely Domain 1, 2 and 3. Efficiency criteria include the standarderror of the estimates (SE) and coefficient of variation (CV) Computed for the study population ofsize 1052 households consisting of domain size of 885, 151 and 16 and domain samples sizes of 167,29 and 3 respectively for Domains 1, 2 and 3. The estimates produced by HT estimator GREGestimator performs better than HT estimator with domain

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13

Pawlas, Zbynek, and Marketa Zikmundova. "A COMPARISON OF NONPARAMETRIC ESTIMATORS FOR LENGTH DISTRIBUTION IN LINE SEGMENT PROCESSES." Image Analysis & Stereology 38, no. 2 (July 18, 2019): 121. http://dx.doi.org/10.5566/ias.1889.

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We study nonparametric estimation of the length distribution for stationary line segment processes in the d-dimensional Euclidean space. Several methods have been proposed in the literature. We review different approaches (Horvitz-Thompson type estimator, reduced-sample estimator, Kaplan-Meier estimator, nonparametric maximum likelihood estimator, stochastic restoration estimation) and compare the finite sample behaviour by means of a simulation study for stationary line segment processes in 2D and 3D. Several data generating processes (Poisson point process, Matérn cluster process and Matérn hard-core process II) are considered with both independent and dependent segments. Our finite sample comparison reveals that the nonparametric likelihood estimator provides the most preferable method which works reasonably also if its assumptions are not satisfied.

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14

Kott, Phillip S. "Model-Based Finite Population Correction for the Horvitz-Thompson Estimator." Biometrika 75, no. 4 (December 1988): 797. http://dx.doi.org/10.2307/2336324.

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15

KOTT, PHILLIP S. "Model-based finite population correction for the Horvitz—Thompson estimator." Biometrika 75, no. 4 (1988): 797–99. http://dx.doi.org/10.1093/biomet/75.4.797.

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16

Patel, P. A., and Jigna S. Patel. "A Monte Carlo comparison of some variance estimators of the Horvitz–Thompson estimator." Journal of Statistical Computation and Simulation 80, no. 5 (May 2010): 489–502. http://dx.doi.org/10.1080/00949650902718325.

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17

Mauro, Francisco, Vicente J. Monleon, Andrew N. Gray, Olaf Kuegler, Hailemariam Temesgen, Andrew T. Hudak, Patrick A. Fekety, and Zhiqiang Yang. "Comparison of Model-Assisted Endogenous Poststratification Methods for Estimation of Above-Ground Biomass Change in Oregon, USA." Remote Sensing 14, no. 23 (November 28, 2022): 6024. http://dx.doi.org/10.3390/rs14236024.

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Quantifying above-ground biomass changes, ΔAGB, is key for understanding carbon dynamics. National Forest Inventories, NFIs, aims at providing precise estimates of ΔAGB relying on model-assisted estimators that incorporate auxiliary information to reduce uncertainty. Poststratification estimators, PS, are commonly used for this task. Recently proposed endogenous poststratification, EPS, methods have the potential to improve the precision of PS estimates of ΔAGB. Using the state of Oregon, USA, as a testing area, we developed a formal comparison between three EPS methods, traditional PS estimators used in the region, and the Horvitz-Thompson, HT, estimator. Results showed that gains in performance with respect to the HT estimator were 9.71% to 19.22% larger for EPS than for PS. Furthermore, EPS methods easily accommodated a large number of auxiliary variables, and the inclusion of independent predictions of ΔAGB as an additional auxiliary variable resulted in further gains in performance.

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18

Ghosh, Malay, and David Haziza. "Revisiting Basu's Circus Example: Another Look at the Horvitz-Thompson Estimator." Calcutta Statistical Association Bulletin 68, no. 1-2 (May 2016): 33–37. http://dx.doi.org/10.1177/0008068316634977.

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19

Berger, Yves G. "Rate of convergence to normal distribution for the Horvitz-Thompson estimator." Journal of Statistical Planning and Inference 67, no. 2 (April 1998): 209–26. http://dx.doi.org/10.1016/s0378-3758(97)00107-9.

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20

Berger, Yves G. "Rate of convergence for asymptotic variance of the Horvitz–Thompson estimator." Journal of Statistical Planning and Inference 74, no. 1 (October 1998): 149–68. http://dx.doi.org/10.1016/s0378-3758(98)00107-4.

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21

Cheruiyot, Langat Reuben, Odhiambo Romanus Otieno, and George O. Orwa. "A Boundary Corrected Non-Parametric Regression Estimator for Finite Population Total." International Journal of Statistics and Probability 8, no. 3 (April 27, 2019): 83. http://dx.doi.org/10.5539/ijsp.v8n3p83.

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This study explores the estimation of finite population total. For many years design-based approach dominated the scene in statistical inference in sample surveys. The scenario has since changed with emergence of the other approaches (Model-Based, Model-Assisted and the Randomization-Assisted), which have proved to rival the conventional approach. This paper focuses on a model based approach. Within this framework a nonparametric regression estimator for finite population total is developed. The nonparametric technique has been found from previous studies to be advantageous than its parametric counterpart in terms of robustness and flexibility.  Kernel smoother has been used in construction of the estimator. The challenge of the boundary problem encountered with the Nadaraya-Watson estimator has been addressed by modifying it using reflection technique. The performance of the proposed estimator has been compared to the design-based Horvitz Thompson estimator and the model –based nonparametric regression estimator proposed by (Dorfman, 1992) and the ratio estimator using simulated data.

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22

Adhikary, Arun Kumar. "On optimality of the horvitz-thompson estimator under a markov process model." Communications in Statistics - Theory and Methods 20, no. 7 (January 1991): 2291–97. http://dx.doi.org/10.1080/03610929108830631.

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23

Delevoye, Angèle, and Fredrik Sävje. "Consistency of the Horvitz–Thompson estimator under general sampling and experimental designs." Journal of Statistical Planning and Inference 207 (July 2020): 190–97. http://dx.doi.org/10.1016/j.jspi.2019.12.002.

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24

Dol, Wietse, Ton Steerneman, and Tom Wansbeek. "Matrix algebra and sampling theory: The case of the Horvitz-Thompson estimator." Linear Algebra and its Applications 237-238 (April 1996): 225–38. http://dx.doi.org/10.1016/0024-3795(95)00781-4.

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Frank, Bryce, and Vicente J. Monleon. "Comparison of Variance Estimators for Systematic Environmental Sample Surveys: Considerations for Post-Stratified Estimation." Forests 12, no. 6 (June 11, 2021): 772. http://dx.doi.org/10.3390/f12060772.

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The estimation of the sampling variance of point estimators under two-dimensional systematic sampling designs remains a challenge, and several alternative variance estimators have been proposed in the past few decades. In this work, we compared six alternative variance estimators under Horvitz-Thompson (HT) and post-stratification (PS) point estimation regimes. We subsampled a multitude of species-specific forest attributes from a large, spatially balanced national forest inventory to compare the variance estimators. A variance estimator that assumes a simple random sampling design exhibited positive relative bias under both HT and PS point estimation regimes ranging between 1.23 to 1.88 and 1.11 to 1.78 for HT and PS, respectively. Alternative estimators reduced this positive bias with relative biases ranging between 1.01 to 1.66 and 0.90 to 1.64 for HT and PS, respectively. The alternative estimators generally obtained improved efficiencies under both HT and PS, with relative efficiency values ranging between 0.68 to 1.28 and 0.68 to 1.39, respectively. We identified two estimators as promising alternatives that provide clear improvements over the simple random sampling estimator for a wide variety of attributes and under HT and PS estimation regimes.

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26

Dirdaitė, Ieva, and Danutė Krapavickaitė. "Application of Balanced Sampling, Non-Response and Calibrated Estimator." Lietuvos statistikos darbai 55, no. 1 (December 20, 2016): 81–90. http://dx.doi.org/10.15388/ljs.2016.13870.

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The aim of this paper is to study the interplay between balanced sampling, non-response and calibratedestimator by simulation. The results of seven strategies, embracing a combination of balanced sampling via the cubemethod, simple random cluster sampling, adjustment for non-response, Horvitz–Thompson estimator of the total andcalibration of design weights, are compared. Auxiliary information is used for all strategies at least at one of the stages(sampling or estimation). This auxiliary information consists of indicator variables for sex, age groups and urban/ruralliving area, and their totals. Real Labour Force Survey data of Statistics Lithuania are used for simulation. Bias, varianceand relative mean squared error are measures of accuracy for the comparison of results.

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Stehman, Stephen V., and W. Scott Overton. "Comparison of Variance Estimators of the Horvitz-Thompson Estimator for Randomized Variable Probability Systematic Sampling." Journal of the American Statistical Association 89, no. 425 (March 1994): 30–43. http://dx.doi.org/10.1080/01621459.1994.10476443.

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McConville, Kelly S., Gretchen G. Moisen, and Tracey S. Frescino. "A Tutorial on Model-Assisted Estimation with Application to Forest Inventory." Forests 11, no. 2 (February 22, 2020): 244. http://dx.doi.org/10.3390/f11020244.

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National forest inventories in many countries combine expensive ground plot data with remotely-sensed information to improve precision in estimators of forest parameters. A simple post-stratified estimator is often the tool of choice because it has known statistical properties, is easy to implement, and is intuitive to the many users of inventory data. Because of the increased availability of remotely-sensed data with improved spatial, temporal, and thematic resolutions, there is a need to equip the inventory community with a more diverse array of statistical estimators. Focusing on generalized regression estimators, we step the reader through seven estimators including: Horvitz Thompson, ratio, post-stratification, regression, lasso, ridge, and elastic net. Using forest inventory data from Daggett county in Utah, USA as an example, we illustrate how to construct, as well as compare the relative performance of, these estimators. Augmented by simulations, we also show how the standard variance estimator suffers from greater negative bias than the bootstrap variance estimator, especially as the size of the assisting model grows. Each estimator is made readily accessible through the new R package, mase. We conclude with guidelines in the form of a decision tree on when to use which an estimator in forest inventory applications.

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Kansanen, Kasper, Petteri Packalen, Timo Lähivaara, Aku Seppänen, Jari Vauhkonen, Matti Maltamo, and Lauri Mehtätalo. "Refining and evaluating a Horvitz–Thompson-like stand density estimator in individual tree detection based on airborne laser scanning." Canadian Journal of Forest Research 52, no. 4 (April 2022): 527–38. http://dx.doi.org/10.1139/cjfr-2021-0123.

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Horvitz–Thompson-like stand density estimation is a method for estimating the stand density from tree crown objects extracted from airborne laser scanning data through individual tree detection. The estimator is based on stochastic geometry and mathematical morphology of the (planar) set formed by the detected tree crowns. This set is used to approximate the detection probabilities of trees. These probabilities are then used to calculate the estimate. The method includes a tuning parameter, which needs to be known to apply the method. We present a refinement of the method to allow more general detection conditions than those of previous papers. We also present and discuss the methods for estimating the tuning parameter of the estimator using a functional k-nearest neighbors method. We test the model fitting and prediction in two spatially separate data sets and examine the plot-level accuracy of estimation. The estimator produced a 13% lower RMSE (root-mean-square error) than the benchmark method in an external validation data set. We also analyze the effects of similarity and dissimilarity of training and validation data on the results.

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Xu, Mengxuan, Victoria Landsman, and Barry I. Graubard. "Estimation of Domain Means from Business Surveys in the Presence of Stratum Jumpers and Nonresponse." Journal of Official Statistics 37, no. 4 (December 1, 2021): 1059–78. http://dx.doi.org/10.2478/jos-2021-0045.

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Abstract Misclassified frame records (also called stratum jumpers) and low response rates are characteristic for business surveys. In the context of estimation of the domain parameters, jumpers may contribute to extreme variation in sample weights and skewed sampling distributions of the estimators, especially for domains with a small number of observations. There is limited literature about the extent to which these problems may affect the performance of the ratio estimators with nonresponse-adjusted weights. To address this gap, we designed a simulation study to explore the properties of the Horvitz-Thompson type ratio estimators, with and without smoothing of the weights, under different scenarios. The ratio estimator with propensity-adjusted weights showed satisfactory performance in all scenarios with a high response rate. For scenarios with a low response rate, the performance of this estimator improved with an increase in the proportion of jumpers in the domain. The smoothed estimators that we studied performed well in scenarios with non-informative weights, but can become markedly biased when the weights are informative, irrespective of response rate. We also studied the performance of the ’doubled half’ bootstrap method for variance estimation. We illustrated an application of the methods in a real business survey.

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Ba̧k, Tomasz. "An extension of Horvitz–Thompson estimator used in adaptive cluster sampling to continuous universe." Communications in Statistics - Theory and Methods 46, no. 19 (September 21, 2016): 9777–86. http://dx.doi.org/10.1080/03610926.2016.1218028.

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32

Schreuder, H. T., Z. Ouyang, and M. Williams. "Point-Poisson, point-pps, and modified point-pps sampling: efficiency and variance estimation." Canadian Journal of Forest Research 22, no. 8 (August 1, 1992): 1071–78. http://dx.doi.org/10.1139/x92-142.

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Modified point-pps (probability proportional to size) sampling selects at least one sample tree per point and yields a fixed sample size. Point-Poisson sampling is as efficient as this modified procedure but less efficient than regular point-pps sampling in a simulation study estimating total volume using either the Horvitz–Thompson (ŶHT) or the weighted regression estimator (Ŷwr). Point-pps sampling is somewhat more efficient than point-Poisson sampling for all estimators except ŶHT, and point-Poisson sampling is always somewhat more efficient than modified point-pps sampling across.all estimators. For board foot volume the regression estimators are more efficient than ŶHT for all three procedures. Point-pps sampling is always most efficient, except for ŶHT, and point-Poisson sampling is always more efficient than the modified point-pps procedure. We recommend using Ŷgr (generalized regression estimator), Ŷwr, or ŶHT for total volume and Ŷgr for board foot volume. Three variance estimators estimate the variances of the regression estimates with small bias; we recommend the simple bootstrap variance estimator because it is simple to compute and does as well as its two main competitors. It does well for ŶHT, too, for all three procedures and should be used for ŶHT in point-Ppisson sampling in preference to the Grosenbaugh variance approximation. An unbiased variance estimator is given for ŶHT with the modified point-pps procedure, but the simple bootstrap variance is equally good.

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Quatember, Andreas. "The Finite Population Bootstrap - From the Maximum Likelihood to the Horvitz-Thompson Approach." Austrian Journal of Statistics 43, no. 2 (June 11, 2014): 93–102. http://dx.doi.org/10.17713/ajs.v43i2.10.

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The finite population bootstrap method is used as a computer-intensive alternative to estimate the sampling distribution of a sample statis-tic. The generation of a so-called “bootstrap population” is the necessarystep between the original sample drawn and the resamples needed to mimicthis distribution. The most important question for researchers to answer ishow to create an adequate bootstrap population, which may serve as a close-to-reality basis for the resampling process. In this paper, a review of someapproaches to answer this fundamental question is presented. Moreover, anapproach based on the idea behind the Horvitz-Thompson estimator allow-ing not only whole units in the bootstrap population but also parts of wholeunits is proposed. In a simulation study, this method is compared with a moreheuristic technique from the bootstrap literature.

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Marino, Mario, and Silvia Pacei. "The Small Area Estimation of Economic Security: A Proposal." International Journal of Statistics and Probability 12, no. 3 (May 23, 2023): 8. http://dx.doi.org/10.5539/ijsp.v12n3p8.

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The objective of this work is to propose a small area estimation strategy for an economic security indicator. In the last decade the interest for the measurement of economic security or insecurity has grown constantly, especially since the financial crisis of 2008 and the pandemic period. In this work, economic security is measures through a longitudinal indicator that compares levels of equivalized household income over time. To solve a small area estimation problem, due to possible sample sizes too low in some areas, a small area estimation strategy is suggested to obtain reliable estimates of the indicator of interest. We consider small area models specified at area level. Besides the basic Fay-Herriot area-level model, we propose to consider some longitudinal extensions, including time-specific random effects following an AR(1) process or an MA(1) process. A simulation study based on EU-SILC data shows that all the small area models considered provide a significant efficiency gain with respect to the Horvitz-Thompson estimator, especially the small area model with MA(1) specification for random effects.

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Shahbaz, Muhammad Qaiser, and Muhammad Hanif. "A New Approximate Formula for Variance of Horvitz–Thompson Estimator using first order Inclusion Probabilities." Pakistan Journal of Statistics and Operation Research 3, no. 1 (January 1, 2007): 59. http://dx.doi.org/10.18187/pjsor.v3i1.78.

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Gökpinar, Fikri, and Yaprak Arzu Özdemir. "A Horvitz-Thompson Estimator of the Population Mean Using Inclusion Probabilities of Ranked Set Sampling." Communications in Statistics - Theory and Methods 41, no. 6 (March 15, 2012): 1029–39. http://dx.doi.org/10.1080/03610926.2010.533235.

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Lin, Mingkai, Wenzhong Li, Lynda J. Song, Cam-Tu Nguyen, Xiaoliang Wang, and Sanglu Lu. "SAKE." ACM Transactions on Knowledge Discovery from Data 15, no. 4 (June 2021): 1–21. http://dx.doi.org/10.1145/3441646.

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Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network are unpractical and computationally expensive. In this article, we propose a novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity. Specifically, we develop a Horvitz–Thompson estimate for Katz centrality by using a multi-round sampling approach and deriving an unbiased mean value estimator. We further propose SAKE , a S ampling-based A lgorithm for fast K atz centrality E stimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. Extensive evaluation experiments based on four real-world networks show that the proposed algorithm can estimate Katz centralities for partial vertices with low sampling rate, low computation time, and it works well in identifying high influence vertices in social networks.

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Zardetto, Diego. "ReGenesees: an Advanced R System for Calibration, Estimation and Sampling Error Assessment in Complex Sample Surveys." Journal of Official Statistics 31, no. 2 (June 1, 2015): 177–203. http://dx.doi.org/10.1515/jos-2015-0013.

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Abstract ReGenesees is a new software system for design-based and model-assisted analysis of complex sample surveys, based on R. As compared to traditional estimation platforms, it ensures easier and safer usage and achieves a dramatic reduction in user workload for both the calibration and the variance estimation tasks. Indeed, ReGenesees allows the specification of calibration models in a symbolic way, using R model formulae. Driven by this symbolic metadata, the system automatically and transparently generates the right values and formats for the auxiliary variables at the sample level, and assists the user in defining and calculating the corresponding population totals. Moreover, ReGenesees can handle arbitrary complex estimators, provided they can be expressed as differentiable functions of Horvitz-Thompson or calibration estimators of totals. Complex estimators can be defined in a completely free fashion: the user only needs to provide the system with the symbolic expression of the estimator as a mathematical function. ReGenesees is in fact able to automatically linearize such complex estimators, so that the estimation of their variance comes at no cost at all to the user. Remarkably, all the innovative features sketched above leverage a particular strong point of the R programming language, namely its ability to process symbolic information.

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Fattorini, Lorenzo, Marzia Marcheselli, Caterina Pisani, and Luca Pratelli. "Design-based consistency of the Horvitz–Thompson estimator under spatial sampling with applications to environmental surveys." Spatial Statistics 35 (March 2020): 100404. http://dx.doi.org/10.1016/j.spasta.2019.100404.

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Corona, P., R. M. Di Biase, L. Fattorini, and M. D’Amati. "A Monte Carlo appraisal of tree abundance and stand basal area estimation in forest inventories based on terrestrial laser scanning." Canadian Journal of Forest Research 49, no. 1 (January 2019): 41–52. http://dx.doi.org/10.1139/cjfr-2017-0462.

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Non-detection of trees is an important issue when using single-scan TLS in forest inventories. A hybrid inference approach is adopted. Quoting from distance sampling, a detection function is assumed, so that the inclusion probability of each tree included within each plot can be determined. A simulation study is performed to compare the TLS-based estimators corrected and uncorrected for non-detection with the Horvitz–Thompson estimator based on conventional plot sampling, in which all the trees within plots are recorded. Results show that single-scan TLS provides more efficient estimators with respect to those provided by the conventional plot sampling in the case of low-density forests when no distance sampling correction is performed. In low-density forests, uncorrected estimators lead to a small bias (1%–6%), increasing with plot size. Therefore, care must be taken in enlarging the plot radius too much. The bias increases in forests with clustered spatial structures and in dense forests, where the bias levels (30%–50%) deteriorate the performance of uncorrected estimators. Even if the bias-corrected estimators prove to be effective in reducing the bias (below 15%), these reductions are not sufficient to outperform conventional plot sampling. Therefore, there is no convenience in using TLS-based estimation in high-density forests.

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Suesse, Thomas, and Ray Chambers. "Using Social Network Information for Survey Estimation." Journal of Official Statistics 34, no. 1 (March 1, 2018): 181–209. http://dx.doi.org/10.1515/jos-2018-0009.

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Abstract Model-based and model-assisted methods of survey estimation aim to improve the precision of estimators of the population total or mean relative to methods based on the nonparametric Horvitz-Thompson estimator. These methods often use a linear regression model defined in terms of auxiliary variables whose values are assumed known for all population units. Information on networks represents another form of auxiliary information that might increase the precision of these estimators, particularly if it is reasonable to assume that networked population units have similar values of the survey variable. Linear models that use networks as a source of auxiliary information include autocorrelation, disturbance, and contextual models. In this article we focus on social networks, and investigate how much of the population structure of the network needs to be known for estimation methods based on these models to be useful. In particular, we use simulation to compare the performance of the best linear unbiased predictor under a model that ignores the network with model-based estimators that incorporate network information. Our results show that incorporating network information via a contextual model seems to be the most appropriate approach. We also show that one does not need to know the full population network, but that knowledge of the partial network linking the sampled population units to the non-sampled population units is necessary. Finally, we also provide an estimator for the mean-squared error to make an informed decision about using the contextual information, as well as the results showing that this adaptive strategy leads to higher precision.

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Younis, Faryal, and Javid Shabbir. "Generalized ratio-type and ratio-exponential-type estimators for population mean under modified Horvitz-Thompson estimator in adaptive cluster sampling." Journal of Statistical Computation and Simulation 89, no. 8 (March 4, 2019): 1505–15. http://dx.doi.org/10.1080/00949655.2019.1586905.

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Okamura, Hiroshi, Toshihide Kitakado, and Mitsuyo Mori. "An improved method for line transect sampling in Antarctic minke whale surveys." J. Cetacean Res. Manage. 7, no. 2 (March 15, 2023): 97–106. http://dx.doi.org/10.47536/jcrm.v7i2.742.

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The series of abundance estimates for Antarctic minke whales obtained using standard line transect methods from IWC/SOWER surveys imply drastic (and probably unrealistic) changes in true abundance. One possible factor is that the detection probability on the trackline, g(0), may have decreased with the introduction of inexperienced observers in the most recent surveys. Additionally, mean observed school size may have decreased in the third circumpolar survey in comparison with the second survey. This paper introduces an extended and generalised hazard probability model without the assumption that g(0)=1 to estimate true school size distribution in the population. The proposed method uses a survey design that combines the use of both passing mode with independent observers and closing mode in which the vessel turns off the trackline and closes with the sighting for confirmation of school size and species. The abundance estimate is based on the Horvitz-Thompson estimator in an unequal detectability sampling scheme. The method is applied to the IDCR/SOWER dataset of Antarctic minke whales for illustrative purposes.

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Dessard, H., and A. Bar-Hen. "Experimental design for spatial sampling applied to the study of tropical forest regeneration." Canadian Journal of Forest Research 35, no. 5 (May 1, 2005): 1149–55. http://dx.doi.org/10.1139/x04-187.

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For practical reasons, estimating seed production in tropical forest is only possible by sampling. Classical sampling designs (random or systematic) give poor estimations of seed abundance. The spatial disposition of the trees, combined with nonuniform seed dispersal, leads to a highly heterogeneous spatial distribution of the seeds. We propose a random stratified sampling design based on a model that takes account of seed dispersal processes and the location of the trees. We assume a gamma distribution for dispersal distances. The overall seed dispersal area is divided into adjacent quadrats. In each quadrat, the number of seeds follows a Poisson distribution with the mean derived from the model. We estimate model parameters from the results of a previous study and give the variance of the HorvitzThompson estimator of population total for stratified and random sampling designs. A simulation study is used to find the optimal number of strata, and the performance of the sampling design is evaluated. For each model, we compared the variance of the estimator of population total obtained with the stratified sampling design with that obtained with the random sampling design with the same sample size. The stratified sampling design is, on average, 25 times as precise as the random sampling design.

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Baffetta, F., P. Corona, and L. Fattorini. "Design-based diagnostics for k-NN estimators of forest resourcesThis article is one of a selection of papers from Extending Forest Inventory and Monitoring over Space and Time." Canadian Journal of Forest Research 41, no. 1 (January 2011): 59–72. http://dx.doi.org/10.1139/x10-157.

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The k-nearest neighbours (k-NN) method constitutes a possible approach to improve the precision of the Horvitz–Thompson estimator of a single interest variable using auxiliary information at the estimation stage. Improvements are likely to occur when the neighbouring structure in the space of auxiliary variables is similar to the neighbouring structure in the space of the survey variables. Populations suitable for k-NN can be identified via the scores of the first principal component computed on the variance–covariance matrix of auxiliary variables. If the first principal component explains a large portion of the whole variability, distances among scores provide good approximations of distances in the space of auxiliary variables in such a way that the effectiveness of k-NN can be assessed by plotting the first principal component scores versus the sampled values of each of the interest variables. Monotone relationships with high values of Spearman’s correlation coefficients should denote effectiveness. Otherwise, when the first principal component explains small fractions of the total variation, an index that directly quantifies the similarity between the neighbouring structure in the space of interest and auxiliary variables is proposed. The validity of the proposed diagnostics is theoretically argued and empirically proven by a simulation study performed on a wide range of artificial and real populations.

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Janusz, Bartłomiej. "APPLICATION OF THE STRATEGY COMBINING MONETARY UNIT SAMPLING AND THE HORVITZ- THOMPSON ESTIMATOR OF ERROR AMOUNT IN AUDITING - RESULTS OF A SIMULATION STUDY." Statistics in Transition New Series 20, no. 2 (2019): 85–106. http://dx.doi.org/10.21307/stattrans-2019-016.

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Givens, Geof, J. Craig George, Robert Suydam, and Barbara Tudor. "Bering-Chukchi-Beaufort Seas bowhead whale (Balaena mysticetus) abundance estimate from the 2019 ice-based survey." J. Cetacean Res. Manage. 22, no. 1 (October 21, 2021): 61–73. http://dx.doi.org/10.47536/jcrm.v22i1.230.

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An ice-based visual survey of the Bering-Chukchi-Beaufort Seas stock of bowhead whales (Balaena mysticetus) was conducted in spring 2019 near UtqiaÄ¡vik (formerly Barrow), Alaska. A Horvitz-Thompson-type estimator is used to estimate population abundance from the resulting data, correcting for detection probabilities, whale availability within visual range, and whale passage during periods of missed effort. Analytical methods mirror those used by Givens et al. (2016) for the 2011 survey as much as possible; however, unlike 2011, no simultaneous acoustic monitoring was conducted in 2019, so the availability correction factor had to be estimated from past years. The estimated abundance was 12,505 with 95% confidence interval of (7,994, 19,560) and a CV of 0.228. This estimated abundance is markedly lower than the 2011 estimate of 16,820, but the 2019 confidence interval wholly encompasses the 2011 interval. We do not interpret this finding as evidence of a decline for many reasons including: highly unusual ice conditions, an unusual migration route that was sometimes too distant from observers to detect whales, failure to conduct watch because of closed leads during the early weeks of the migration when numerous whales likely passed, an unusually short perch, and huntersâ€™ heavy use of powered skiffs near the observation perch which likely disturbed the whales during the survey. Furthermore, bowhead health assessment information for 2019 suggests that harvested bowheads did not exhibit obvious reductions in health condition, and aerial surveys in summer 2019 indicated high calf production (Stimmelmayr et al. 2020). Despite the challenges of the 2019 survey, the estimate is adequate for use with the International Whaling Commissionâ€™s management procedure and complies with the survey requirements of the Aboriginal Whaling Scheme.

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Wąs, Adam, and Pawel Kobus. "Factors differentiating the level of crop insurance at Polish farms." Agricultural Finance Review 78, no. 2 (April 3, 2018): 209–22. http://dx.doi.org/10.1108/afr-06-2017-0054.

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Purpose The purpose of this paper is to identify the factors that determine demand for crop insurance in Poland. Design/methodology/approach To examine the determinants of decisions regarding crop insurance, the authors used logistic regression. The base source of data for the analysis was the 2013 FADN sample. The scale of yield losses, the indemnities received and the Arrow-Pratt risk aversion coefficient were examined in a representative sample of farms in consecutive years in the period 2004-2013. Findings Losses are the major determinants of crop insurance uptake. Additionally, it was observed that the economic determinants are in line with the expected utility theory, while contrary to expectations, farmer’s characteristics such as education level, age or even risk aversion did not prove to have any influence on crop insurance uptake. Research limitations/implications The FADN sample is representative as regards the type of farming, economic size of farm and location of the farm. Every farm in the sample represents a specific number of similar farms in the population. However, it must be emphasised that the representativeness of the sample with respect to other determinants, e.g., yield losses in previous years, using crop insurance or the farmers’ age and education has not been verified due to lack of data characterizing the general population with regard to these factors. Practical implications It could be argued that the system of crop insurance subsidies should be targeted to encourage the farmers who previously had not used insurance to join the system. Originality/value The paper presents the analysis of crop insurance uptake in a country with a strongly polarised agriculture. The Polish farm sector consists of 1.4 million farms with sizes ranging from 1 ha to over a few thousands hectares. The research is based on a data set of 5,202 farms which contains data from ten years (2004-2013). The novelty of the methodological approach is that it includes information on the number of farms represented by every farm in the FADN sample in the Horvitz-Thompson estimator in order to achieve results which are valid for the general population of Polish farms.

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Espejo, M. Ruiz. "Diseños muestrales admisibles para el estimador Horvitz-Thompson." Trabajos de Estadistica 2, no. 1 (March 1987): 45–50. http://dx.doi.org/10.1007/bf02864817.

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Barabesi, Lucio, Giancarlo Diana, and Pier Francesco Perri. "Horvitz-Thompson estimation with randomized response and nonresponse." Model Assisted Statistics and Applications 9, no. 1 (January 1, 2014): 3–10. http://dx.doi.org/10.3233/mas-130274.

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