Relevant bibliographies by topics / Ratio estimator

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Ratio estimator'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Ratio estimator"

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YADAV, SUBHASH KUMAR, DIKSHA ARYA, TUBA KOC, and TOLGA ZAMAN. "AN EFFICIENT FAMILY OF RATIO TYPE ESTIMATORS FOR SIMPLE RANDOM SAMPLING." Journal of Science and Arts 24, no. 1 (2024): 69–94. http://dx.doi.org/10.46939/j.sci.arts-24.1-a07.

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The study provides an enhanced estimation of the population mean using known information on an auxiliary variable. An enhanced class of estimators is suggested for the same. The proposed estimator's bias and mean squared error (MSE) are calculated up to the first order of approximation. The optimum values of the characterizing constants are obtained by minimizing the MSE of the proposed estimator. The minimum MSE and the bias values are achieved by optimising the characterizing scalar. The MSE of the proposed estimator has also been compared both conceptually and empirically with the MSEs of c
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Lui, Kung-Jong. "Notes on Use of the Composite Estimator: an Improvement of the Ratio Estimator." Journal of Official Statistics 36, no. 1 (2020): 137–49. http://dx.doi.org/10.2478/jos-2020-0007.

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AbstractThis article discusses use of the composite estimator with the optimal weight to reduce the variance (or the mean-squared-error, MSE) of the ratio estimator. To study the practical usefulness of the proposed composite estimator, a Monte Carlo simulation is performed comparing the bias and MSE of composite estimators (with estimated optimal weight and with known optimal weight) with those of the simple expansion and the ratio estimators. Two examples, one regarding the estimation of dead fir trees via an aerial photo and the other regarding the estimation of the average sugarcane acres
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Shaheen, Nazia, Muhammad Nouman Qureshi, Osama Abdulaziz Alamri, and Muhammad Hanif. "Optimized inferences of finite population mean using robust parameters in systematic sampling." PLOS ONE 18, no. 1 (2023): e0278619. http://dx.doi.org/10.1371/journal.pone.0278619.

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In this article, we have proposed a generalized estimator for mean estimation by combining the ratio and regression methods of estimation in the presence of auxiliary information using systematic sampling. We incorporated some robust parameters of the auxiliary variable to obtain precise estimates of the proposed estimator. The mathematical expressions for bias and mean square error of proposed the estimator are derived under large sample approximation. Many other generalized ratio and product-type estimators are obtained from the proposed estimator using different choices of scalar constants.
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Cobb, Adam D., Brian Matejek, Daniel Elenius, Anirban Roy, and Susmit Jha. "Direct Amortized Likelihood Ratio Estimation." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 18 (2024): 20362–69. http://dx.doi.org/10.1609/aaai.v38i18.30018.

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We introduce a new amortized likelihood ratio estimator for likelihood-free simulation-based inference (SBI). Our estimator is simple to train and estimates the likelihood ratio using a single forward pass of the neural estimator. Our approach directly computes the likelihood ratio between two competing parameter sets which is different from the previous approach of comparing two neural network output values. We refer to our model as the direct neural ratio estimator (DNRE). As part of introducing the DNRE, we derive a corresponding Monte Carlo estimate of the posterior. We benchmark our new r
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K, Oguagbaka, S., Okoli, O. C, and Aronu, C. O. "Ratio estimator for double sampling procedure with non-response: An empirical study." International Journal of Basic and Applied Science 12, no. 4 (2024): 148–58. http://dx.doi.org/10.35335/ijobas.v12i4.281.

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This study proposes a ratio-type estimator for population mean estimation using auxiliary variables with double sampling in the presence of non-response. The study provides expressions for the constant, bias, and mean square errors (MSE) of the proposed estimator and compares it with ten existing estimators. The study employed the secondary source of data collection to evaluate the efficiency of the proposed and existing estimators by analyzing five natural populations from three different sources. The performance of ten (10) estimators was considered in this study. The findings suggest that t
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Olasunkanmi Muili, Jamiu, and A. Audu. "Estimation of Finite Population Mean of Median Based Using Power Transformation." Oriental Journal of Physical Sciences 6, no. 1-2 (2022): 26–31. http://dx.doi.org/10.13005/ojps06.01-02.05.

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This paper deals with the assessment of finite population mean. An estimator is suggested for estimation of finite population mean of study variable. The purpose of this study is to evolve a ratio-type estimator to enhance the proficiency of the existing estimators considered in the study in sample random sampling without replacement using information of auxiliary variable. Expressions of the bias and mean square error (MSE) of the proposed estimator was derived by Taylor series method. The efficiency conditions under which the proposed ratio-type estimator is better than sample mean, ratio es
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Muhammad, Isah. "Generalized Ratio-Product cum Regression Variance Estimator in Two-Phase Sampling." Central Bank of Nigeria Journal of Applied Statistics 14, no. 2 (2023): 73–101. http://dx.doi.org/10.33429/cjas.14223.4/5.

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This study develops a flexible and efficient generalized ratio-product cum regression-type estimator of population variance utilizing auxiliary variable in two-phase sampling that incorporates the properties of ratio-type and product-type estimators. The properties of the estimator were derived using first order approximation. The theoretical conditions under which the precision and the flexibility of the estimator is better than some classical estimators are also provided. Empirical evidence from five real datasets suggests that the proposed estimator outperforms the classical variance, ratio
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Chami, Peter S., Bernd Sing, and Doneal Thomas. "A Two-Parameter Ratio-Product-Ratio Estimator Using Auxiliary Information." ISRN Probability and Statistics 2012 (October 14, 2012): 1–15. http://dx.doi.org/10.5402/2012/103860.

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We propose a two-parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in the studies of Ray and Sahai (1980), Sahai and Ray (1980), A. Sahai and A. Sahai (1985), and Singh and Espejo (2003).The bias and mean squared error of our proposed estimator are obtained to the first degree of approximation. We derive conditions for the parameters under which the proposed estimator has smaller mean squared error than the sample mean, ratio, and product estimators. We carry out an application showing that the proposed
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Yadav, Pooja, and Mukesh Kumar. "A new Dual to Difference-cum-Ratio Type Exponential Estimator of Population Mean." INTERNATIONAL JOURNAL OF AGRICULTURAL AND STATISTICAL SCIENCES 21, no. 01 (2025): 229. https://doi.org/10.59467/ijass.2025.21.229.

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Auxiliary information is frequently used to improve the efficiency of estimators in sampling theory. With the help of auxiliary information, we can increase the estimator's efficiency and accuracy by incorporating an auxiliary variable. Some of the well-known estimators in this category are ratio estimator, product estimator, regression estimator, exponential ratio estimator and exponential product estimator etc. The major portion of the research in sampling theory revolves around to propose efficient estimators. Dual class of estimators is appropriate and performs better at many occasions. In
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Malik, Sachin, and Rajesh Singh. "Some Improved Multivariate-Ratio-Type Estimators Using Geometric and Harmonic Means in Stratified Random Sampling." ISRN Probability and Statistics 2012 (August 26, 2012): 1–7. http://dx.doi.org/10.5402/2012/509186.

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Auxiliary variable is commonly used in survey sampling to improve the precision of estimates. Whenever there is auxiliary information available, we want to utilize it in the method of estimation to obtain the most efficient estimator. In this paper using multiauxiliary information we have proposed estimators based on geometric and harmonic mean. It was also shown that estimators based on harmonic mean and geometric mean are less biased than Olkin (1958) and Singh (1967) estimators under certain conditions. However, the MSE of Olkin (1958) estimator and geometric and harmonic estimators are sam
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Dissertations / Theses on the topic "Ratio estimator"

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Edvinsson, Simon. "Estimation of the local Hurst function of multifractional Brownian motion : A second difference increment ratio estimator." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-105770.

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In this thesis, a specific type of stochastic processes displaying time-dependent regularity is studied. Specifically, multifractional Brownian motion processes are examined. Due to their properties, these processes have gained interest in various fields of research. An important aspect when modeling using such processes are accurate estimates of the time-varying pointwise regularity. This thesis proposes a moving window ratio estimator using the distributional properties of the second difference increments of a discretized multifractional Brownian motion. The estimator captures the behaviour
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Manno, Michael S. "An evaluation of the odds ratio as an estimator of vaccine efficacy." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0001/MQ28747.pdf.

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Bjerre, Lise M. (Lise Marie). "Analysis of etiologic studies : understanding the Mantel-Haenszel estimator of odds ratio." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22849.

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The present work is an endeavour to gain an understanding of the Mantel-Haenszel (MH) estimator beyond that which can be garnered from textbook consultation. To this end, I explore two aspects of the estimator which cannot be fully understood from the textbooks: the rationale for its weights, and its performance. The first one has to do with the basis for the particular choice of the estimator's weights, and the second one with the estimator's distributional properties and their assessment.<br>The approach to each of the topics is, first, to identify and understand what is presented in the ori
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Sousa, Rita Cristina Pinto de. "Parameter estimation in the presence of auxiliary information." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2013. http://hdl.handle.net/10362/11295.

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Dissertação para obtenção do Grau de Doutora em Estatística e Gestão de Risco, Especialidade em Estatística<br>In survey research, there are many situations when the primary variable of interest is sensitive. The sensitivity of some queries can give rise to a refusal to answer or to false answers given intentionally. Survey can be conducted in a variety of settings, in part dictated by the mode of data collection, and these settings can differ in how much privacy they offer the respondent. The estimates obtained from a direct survey on sensitive questions would be subject to high bias. A va
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Cai, Bing. "The case-crossover design, an efficient rate ratio estimator based on prescription times." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape2/PQDD_0017/MQ55042.pdf.

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Cai, Bing. "The case-crossover design : an efficient rate ratio estimator based on prescription times." Thesis, McGill University, 1999. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=30116.

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The case-crossover design is a new epidemiological method that evolved around binary exposures and the binomial distribution. We develop a new approach of data analysis for this design based on the actual exposure occurrence times, such as those available from computerized prescription databases. Assuming an exponential distribution for the inter-exposure onset times, we derive two new matched-paired estimators of the odds-ratio, one weighted the other unweighted. A simulation study demonstrates that both new estimators based on the exponential distribution are more efficient than the classica
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Sayre, Michelle Marie. "Development of a Block Processing Carrier to Noise Ratio Estimator for the Global Positioning System." Ohio University / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1071063030.

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DE, PAOLA ROSITA. "Median estimation using auxiliary variables." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2012. http://hdl.handle.net/10281/36075.

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In the present study the estimation of the median has been taken into consideration using different methods of analysis. First of all the estimation of the median without auxiliary information is analyzed. Then the method of Kuk and Mak proposed in 1989 is exposed: this way of estimating the median is based on the knowledge of the population median of auxiliary variable X. Another method, which considers the median of the auxiliary variable is the ratio estimator. Then two methods based on the regression estimator are analyzed : the first one considers the regression based on the median
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Top, Alioune. "Estimation paramétriques et tests d'hypothèses pour des modèles avec plusieurs ruptures d'un processus de poisson." Thesis, Le Mans, 2016. http://www.theses.fr/2016LEMA1014/document.

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Ce travail est consacré aux problèmes d’estimation paramétriques, aux tests d’hypothèses et aux tests d’ajustement pour les processus de Poisson non homogènes.Tout d’abord on a étudié deux modèles ayant chacun deux sauts localisés par un paramètre inconnu. Pour le premier modèle la somme des sauts est positive. Tandis que le second a un changement de régime et constant par morceaux. La somme de ses deux sauts est nulle. Ainsi pour chacun de ces modèles nous avons étudié les propriétés asymptotiques de l’estimateur bayésien (EB) et celui du maximum de vraisemblance(EMV). Nous avons montré la co
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Gottfridsson, Anneli. "Likelihood ratio tests of separable or double separable covariance structure, and the empirical null distribution." Thesis, Linköpings universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-69738.

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The focus in this thesis is on the calculations of an empirical null distributionfor likelihood ratio tests testing either separable or double separable covariancematrix structures versus an unstructured covariance matrix. These calculationshave been performed for various dimensions and sample sizes, and are comparedwith the asymptotic χ2-distribution that is commonly used as an approximative distribution. Tests of separable structures are of particular interest in cases when data iscollected such that more than one relation between the components of the observationis suspected. For instance,
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Books on the topic "Ratio estimator"

1

Manno, Michael S. An evaluation of the odds ratio as an estimator of vaccine efficacy. National Library of Canada = Bibliothèque nationale du Canada, 1999.

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Seale, David Andrew. A statistical model of microarray images and an estimator of gene expression ratio. National Library of Canada, 2002.

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L, Musgrave Jeffrey, and United States. National Aeronautics and Space Administration., eds. A neural network-based estimator for the mixture ratio of the space shuttle main engine. National Aeronautics and Space Administration, 1992.

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J, Musgrave, and United States. National Aeronautics and Space Administration., eds. A neural network-based estimator for the mixture ratio of the space shuttle main engine. National Aeronautics and Space Administration, 1992.

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J, Musgrave, and United States. National Aeronautics and Space Administration., eds. A neural network-based estimator for the mixture ratio of the space shuttle main engine. National Aeronautics and Space Administration, 1992.

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Willem W. S. Van Hees. A comparison of two estimates of standard error for a ratio-of-means estimator for a mapped-plot sample design in Southeast Alaska. U.S. Dept. of Agriculture, Forest Service, Pacific Northwest Research Station, 2002.

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1981-, Suzuki Taiji, and Kanamori Takafumi 1971-, eds. Density ratio estimation in machine learning. Cambridge University Press, 2012.

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Cecchetti, Stephen G. Structural estimates of the U.S. sacrifice ratio. Federal Reserve Bank of New York, 1999.

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Tomlinson, George. Confounder measurement error and exposure odds ratio estimation. National Library of Canada = Bibliothèque nationale du Canada, 1993.

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Baccour, Nouha, Anis Koubâa, Claro Noda, et al. Radio Link Quality Estimation in Low-Power Wireless Networks. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00774-8.

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Book chapters on the topic "Ratio estimator"

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Andersen, Per Kragh. "Hazard Ratio Estimator." In International Encyclopedia of Statistical Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-04898-2_284.

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Andersen, Per Kragh. "Hazard Ratio Estimator." In International Encyclopedia of Statistical Science. Springer Berlin Heidelberg, 2025. https://doi.org/10.1007/978-3-662-69359-9_265.

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Vaz, Afonso, Rafael Izbicki, and Rafael Bassi Stern. "Prior Shift Using the Ratio Estimator." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91143-4_3.

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Pokropp, Fritz. "Homogeneous Regression and Ratio-Estimator in Simple Random Sampling." In Mathematische Methoden der Wirtschaftswissenschaften. Physica-Verlag HD, 1999. http://dx.doi.org/10.1007/978-3-662-12433-8_18.

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Janet, Akingbade Toluwalase, and Balogun Oluwafemi Samson. "Class of Exponential Ratio Type Estimator for Population Mean in Adaptive Cluster Sampling." In Optimal Decision Making in Operations Research and Statistics. CRC Press, 2021. http://dx.doi.org/10.1201/9781003106951-12.

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Basmann, R. L., and Hae-Shin Hwang. "A Monte Carlo Study of Structural Estimator Distributions After Performance of Likelihood Ratio Pre-Tests." In Contributions to Econometric Theory and Application. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4613-9016-9_5.

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Li, T., and J. Wang. "W-Ratio Test as an Integer Aperture Estimator: Pull-in Regions and Ambiguity Validation Performance." In International Association of Geodesy Symposia. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10828-5_10.

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Wongyai, Channarong, and Sirima Suwan. "Comparisons of Confidence Interval for a Ratio of Non-normal Variances Using a Kurtosis Estimator." In Structural Changes and their Econometric Modeling. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04263-9_56.

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Zahid, Sara, Asifa Kamal, and Mahnaz Makhdum. "Generalized Dual to Exponential Ratio Type Estimator for the Finite Population Mean in the Presence of Nonresponse." In Promoting Statistical Practice and Collaboration in Developing Countries. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003261148-23.

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Sahu, Pradip Kumar, Santi Ranjan Pal, and Ajit Kumar Das. "Likelihood Ratio Test." In Estimation and Inferential Statistics. Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2514-0_4.

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Conference papers on the topic "Ratio estimator"

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Oladimeji, Olatunji Muhammad, Amos Adedayo Adewara, Femi Emmanuel Amoyedo, Ezekiel Olaoluwa Omole, Peter Onu, and Kehinde Peter Ajewole. "Improved Ratio Estimator under Stratified Simple Random Sampling Using Auxiliary Variable." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10630033.

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Amoyedo, Femi Emmanuel, Akinremi O. Joseph, Timilehim Shaba Gideon, and Joshua Otonritse Okoro. "Enriched Ratio-Cum-Product Estimator Utilizing Ancillary Attribute for Double Sampling." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10629853.

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Nakhutin, Alexander, Nikita Popov, Vladimir Berdin, Andrey Mironov, Anastasia Uledova, and Daria Kozlova. "NATIONAL GREENHOUSE GAS EMISSION FACTORS AT OIL AND GAS CONDENSATE PRODUCTION AND TREATMENT FACILITIES IN RUSSIAN FEDERATION." In 24th SGEM International Multidisciplinary Scientific GeoConference 2024. STEF92 Technology, 2024. https://doi.org/10.5593/sgem2024v/3.2/s06.46.

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Accurate estimation of greenhouse gases in national inventory reports, submitted by countries every year under the UNFCCC and the Paris Agreement is an important task. Fugitive greenhouse gas emissions from oil production, gathering and treatment is a key category in the Russian national inventory report. Total emissions from this category accounted to more than 30 million tons of CO2 equivalent in 2021. Since in Russian inventory the default IPCC emission factors from these operations are used, in the framework of government project �Russian climate monitoring system� new country-specific CH4
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Singh, B. K., Diganta Kalita, and Sanjib Choudhury. "EXPONENTIAL RATIO CUM EXPONENTIAL DUAL TO RATIO ESTIMATOR IN DOUBLE SAMPLING." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics (CMCGS 2014). GSTF, 2014. http://dx.doi.org/10.5176/2251-1911_cmcgs14.05.

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O'Reilly, P. "A neural network air-fuel ratio estimator." In International Conference on Control '94. IEE, 1994. http://dx.doi.org/10.1049/cp:19940127.

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Ali, Hussein F. M., Se-Woong Oh, and Youngshik Kim. "State Estimation of a Robotic Vehicle With Six In-Wheel Drives Using Kalman Filter." In ASME 2020 29th Conference on Information Storage and Processing Systems. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/isps2020-1937.

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Abstract This paper describes an estimation algorithm for a robotic vehicle with articulated suspension (RVAS) to estimate the vehicle velocity and acceleration states, and the tire forces. The RVAS is an unmanned ground vehicle based on a skid steering using an independent in-wheel motor at each wheel. The estimation algorithm consists of five parts. In the first part, a wheel state estimator estimates the wheel rotational speed and its angular acceleration using Kalman filter, which is used to estimate the longitudinal tire force distribution in the second part. The third part is to estimate
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Winick, Kim A. "Cramer-Rao lower bounds on the performance of CCD optical position estimators." In OSA Annual Meeting. Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.fi2.

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The problem of optically estimating an object’s position using a charge coupled device (CCD) array composed of square pixels Δx on a side is analyzed. The object’s image spot at the CCD is assumed to have a Gaussian intensity profile with a 1/e point at a radial distance of 2 σ s from the peak, and the CCD noise is modeled as Poisson distributed dark current shot noise. A 2-D Cramer-Rao bound is developed and used to determine a lower limit for the mean-square error of any unbiased position estimator, and the maximum likelihood estimator is also derived. For the 1-D position estimation problem
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Wang, Xiuheng, Ricardo Augusto Borsoi, Cédric Richard, and Jie Chen. "Change Point Detection with Neural Online Density-Ratio Estimator." In ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023. http://dx.doi.org/10.1109/icassp49357.2023.10095321.

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Lye, Scott Carr Ken, Mohammad Sigit Arifianto, Hoe Tung Yew, Chung Fan Liau, and Kenneth Tze Kin Teo. "Performance of Signal-to-Noise Ratio Estimator with Adaptive Modulation." In 2012 6th Asia Modelling Symposium (AMS 2012). IEEE, 2012. http://dx.doi.org/10.1109/ams.2012.40.

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Windmann, M., and P. M. Krummrich. "Histogram-Based Bit Error Ratio Estimator for Differential Modulation Formats." In 2008 Conference on Optical Fiber Communication - OFC 2008 Collocated National Fiber Optic Engineers. IEEE, 2008. http://dx.doi.org/10.1109/ofc.2008.4528085.

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Reports on the topic "Ratio estimator"

1

van Hees, Willem W. S. A comparison of two estimates of standard error for a ratio-of-means estimator for a mapped-plot sample design in southeast Alaska. U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, 2002. http://dx.doi.org/10.2737/pnw-rn-532.

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Kott, Phillip S. Better Coverage Intervals for Estimators from a Complex Sample Survey. RTI Press, 2020. http://dx.doi.org/10.3768/rtipress.2020.mr.0041.2002.

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Coverage intervals for a parameter estimate computed using complex survey data are often constructed by assuming the parameter estimate has an asymptotically normal distribution and the measure of the estimator’s variance is roughly chi-squared. The size of the sample and the nature of the parameter being estimated render this conventional “Wald” methodology dubious in many applications. I developed a revised method of coverage-interval construction that “speeds up the asymptotics” by incorporating an estimated measure of skewness. I discuss how skewness-adjusted intervals can be computed for
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Glynn, Peter W. Likelihood Ratio Derivative Estimators for Stochastic Systems. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada213787.

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Glynn, Peter W. Likelihood Ratio Gradient Estimation: An Overview. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada197085.

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Reyes-Tagle, Gerardo, and Jorge E. Muñoz-Ayala. Debt and Economic Growth: Does Size Matter? Evidence from Dynamic Parametric and Static Non-parametric Approaches. Inter-American Development Bank, 2023. http://dx.doi.org/10.18235/0004818.

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This paper provides new evidence on the effect of debt on economic growth through two alternative methodological approaches. On the one hand, by using a panel error correction model with a sample of 130 countries between 1980 and 2020, we found evidence of the existence of a range of debt-to-GDP ratios for which economic growth remains positive after debt surges. This threshold may lie between 32 percent and 136 percent, with optimal economic growth achieved at an 84 percent debt-to-GDP ratio for the whole sample of countries. The error correction form for the economic growth was dynamically c
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Glynn, Peter W., Pierre L'Ecuyer, and Michel Ades. Gradient Estimation for Ratios. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada248453.

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Lindgren, Eric R., Samuel Durbin, Jason Wilke, J. Margraf, and T. A. Dunn. Numerical Estimation of the Spent Fuel Ratio. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1237522.

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Ahmad, M., C. Marcotte, and R. S. Singh. Double Sampling in Estimation of a Ratio. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada160346.

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Panek, Jeffrey, Adrian Huth, James McCarthy, and Alan Krol. PR-312-18208-E02 PRCI White Paper PVMRM Theoretical Issues and Recommended Solutions. Pipeline Research Council International, Inc. (PRCI), 2021. http://dx.doi.org/10.55274/r0012113.

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Abstract:
This white paper demonstrates that AERMOD contains formulation errors and does not currently provide accurate NOx estimates for sources (e.g., natural gas compressor stations) with shorter stacks. The white paper also demonstrates that a new building downwash theory (PRIME2) does provide better agreement with NOx observations than AERMOD's PRIME algorithms. In addition, the white paper shows that PVMRM does not provide accurate estimates of the NO2/NOx ratio as confirmed by Panek et al. (2020) who showed poor agreement between predicted and observed NO2/NOx ratios. The paper concludes that the
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Shanahan, Erin, Rob Daley, Lydia Druin, Kristin Legg, and Sonya Daw. Status of whitebark pine in the Greater Yellowstone Ecosystem: A step-trend analysis with comparisons from 2004 to 2023. National Park Service, 2025. https://doi.org/10.36967/2313989.

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Whitebark pine (Pinus albicaulis) is a high-elevation conifer of the northern Rocky Mountains and the Pacific Northwest. This slow-growing, long-lived conifer influences critical ecosystem functions in subalpine environments, including snow capture, landscape stability, soil amelioration, and overall forest health and resilience. Moreover, its nutritious seeds feed the federally threatened grizzly bear (Ursus arctos), Clark’s nutcracker (Nucifraga columbiana), red squirrel (Tamiasciurus hudsonicus), and other species. However, whitebark pine is declining in high-elevation forests due to severa
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