Classification of Sampling Methods and its Applications in Various Fields

In this paper, we propose a calibration estimator of population mean in stratified sampling using the known mean and variance information from multi-auxiliary variables. The problem of determining the optimum calibrated weights is formulated as a Nonlinear Programming Problem (NLPP) that is solved using the Lagrange multiplier technique. Numerical example with real data is presented to illustrate the computational details of the proposed estimator. A comparison study is also carried out using real and simulated data to evaluate the performance and the usefulness of the proposed estimator. The study reveals that the proposed estimator with multi-auxiliary information is more efficient estimator of the population mean as it provides least estimated variance and highest gain in relative efficiency (RE). References Jean Claude Deville and Carl Erik Sarndal. Calibration estimators in survey sampling. Journal of the American statistical Association, 87(418):376–382, 1992. doi:10.1080/01621459.1992.10475217 . Victor M Estevao and Carl Erik Sarndal. Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74(2):127–147, 2006. doi:110.1111/j.1751-5823.2006.tb00165.x Patrick J Farrell and Sarjinder Singh. Model-assisted higher-order calibration of estimators of variance. Australian and New Zealand Journal of Statistics, 47(3):375–383, 2005. doi:10.1111/j.1467-842X.2005.00402.x Wolfram Research, Inc. Mathematica, Version 11.3. Champaign, IL, 2018. Jong Min Kim, Engin A Sungur, and Tae Young Heo. Calibration approach estimators in stratified sampling. Statistics and probability letters, 77(1):99–103, 2007. doi:10.1016/j.spl.2006.05.015 Phillip S Kott. Using calibration weighting to adjust for nonresponse and coverage errors. Survey Methodology, 32(2):133, 2006. Dinesh K Rao. Mathematical programing in stratified random sampling. PhD thesis, School of Computing, Information and Mathematical Sciences, The University of the South Pacific, Fiji, February 2017. Dinesh K. Rao, Tokaua. Tekabu, and Mohammad G M Khan. New calibration estimators in stratified sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering, pages 66–70. IEEE, 2016. Gurmindar K Singh, Dinesh K Rao, and Mohammed GM Khan. Calibration estimator of population mean in stratified random sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering (APWC on CSE), pages 1–5. IEEE, 2014. Sarjindar Singh, Stephen Horn, and Frank Yu. Estimation of variance of general regression estimator: Higher level calibration approach. Survey Methodology, 24:41–50, 1998. Sarjinder Singh. Advanced Sampling Theory With Applications: How Michael Selected Amy, volume I and II. Kluwer Academic Publishers, Netherlands, 2003. Sarjinder Singh. On the calibration of design weights using a displacement function. Metrika, 75(1):85–107, 2012. doi:10.1007/s00184-010-0316-6 Sarjinder Singh, Stephen Horn, Sadeq Chowdhury, and Frank Yu. Theory and methods: Calibration of the estimators of variance. Australian and New Zealand Journal of Statistics, 41(2):199–212, 1999. doi:10.1111/1467-842X.00074 D S Tracy, S Singh, and R Arnab. Note on calibration in stratified and double sampling. Survey Methodology, 29(1):99–104, 2003. Changbao Wu and Randy R Sitter. A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association, 96(453):185–193, 2001. doi:10.1198/016214501750333054

An unconstrained statistical matching algorithm for combining individual and household level geo-specific census and survey data

This book presents the theory of probability and mathematical statistics at a level suitable for researchers at the frontiers of applied disciplines. Examples and exercises make essential concepts in measure theory and analysis accessible to those with preparation limited to vector calculus. Complete, detailed solutions to all the exercises demonstrate techniques of problem solving and provide immediate feedback. Part I, The Theory of Probability, starts with elementary set theory and proceeds through basic measure and probability, random variables, integration and mathematical expectation. It concludes with an extensive survey of models for distributions of random variables. Part II, The Theory of Statistics, begins with sampling theory and distribution theory for statistics from normal populations, proceeds to asymptotic (large-sample) theory, and on to point and interval estimation and tests of parametric hypotheses. The last three chapters cover tests of nonparametric hypotheses, Bayesian methods, and linear and nonlinear regression. Researchers and graduate students in applied fields such as actuarial science, biostatistics, economics, finance, mathematical psychology, and systems engineering will find this book to be a valuable learning tool and an essential reference. Contents: The Theory of Probability: Probability on Abstract Sets Probability on Sets of Real Numbers Mathematical Expectation Models for Distributions The Theory of Statistics: Sampling Distributions Asymptotic Distribution Theory Estimation Tests of Parametric Hypotheses Tests of Nonparametric Hypotheses A Survey of Bayesian Methods Regression Analysis Readership: Researchers and graduate students in applied fields such as actuarial science, biostatistics, economics, finance, mathematical psychology, and systems engineering. Key Features: Present basic concepts in real and complex analysis and measure theory along with the applications to probability Difficult theoretical points are followed directly by examples and exercises with detailed solutions Provide a survey of Bayesian methods and an extensive treatment of goodness-of-fit tests Suitable learning tool for students and researchers in applied fields for whom a rigorous foundation in probability and statistical inference is essential

The one-dimensional feature-separability model concerning the feature-separability issue of radar emitter signals is proposed based on the probability theory and statistical theory, to evaluate the deinterleaving and recognition capability of extracted features. The proposed method is applied to analyze convention features of radar emitter signals. The theoretical analysis and experimental results show that the proposed model offers a new way to analyze the validity of extracted features, and is valid in both the original feature space and linear-transformed feature space.

We describe a stratified sampling design that combines electronic health records (EHRs) and United States Census (USC) data to construct the sampling frame and an algorithm to enrich the sample with individuals belonging to rarer strata. This design was developed for a multi-site survey that sought to examine patient concerns about and barriers to participating in research studies, especially among under-studied populations (eg, minorities, low educational attainment). We defined sampling strata by cross-tabulating several socio-demographic variables obtained from EHR and augmented with census-block-level USC data. We oversampled rarer and historically underrepresented subpopulations. The sampling strategy, which included USC-supplemented EHR data, led to a far more diverse sample than would have been expected under random sampling (eg, 3-, 8-, 7-, and 12-fold increase in African Americans, Asians, Hispanics and those with less than a high school degree, respectively). We observed that our EHR data tended to misclassify minority races more often than majority races, and that non-majority races, Latino ethnicity, younger adult age, lower education, and urban/suburban living were each associated with lower response rates to the mailed surveys. We observed substantial enrichment from rarer subpopulations. The magnitude of the enrichment depends on the accuracy of the variables that define the sampling strata and the overall response rate. EHR and USC data may be used to define sampling strata that in turn may be used to enrich the final study sample. This design may be of particular interest for studies of rarer and understudied populations.

본 연구에서는 현재 부산시청에서 작성하고 있는 국가승인통계 중 전수조사로 실시하고 있는 해양산업조사의 표본조사 방법에 대한 연구를 다루고 있다. 해양산업조사는 부산시청에서 자체 개발한 전국 최초 해양산업 분야의 국가승인통계로 부산 해양산업 활성화를 위한 기초자료로 활용되고 있다. 해양산업조사의 목적은 부산의 전체 산업에서 해양산업의 비중을 파악하는 것과 해양산업 발전 현안에 있어서 가장 중요한 요인을 파악하는 것이다. 최근 사업체를 대상으로 하는 통계조사의 종류가 다양해짐에 따라 사업체의 응답부담 증가 등 조사환경이 점점 악화되고, 최저임금이 큰 폭으로 상승함에 따라 통계조사에 소요되는 비용이 매년 크게 증가하는 등 향후에는 통계조사 추진에 있어서 여러 가지 난관에 직면할 것으로 예상된다. 본 연구에서는 효율적인 통계조사 추진을 위해 표본조사 방법을 연구하고 모집단에서 층화계통추출법으로 표본을 추출한 다음, 표본에서 얻어진 추정값을 전수조사 결과와 비교하여 표본조사 전환 가능여부에 대해서 살펴보고자 한다.This study deals with the sample survey method of the marine industry survey which is carried out by the preliminary investigation among the national approval statistics currently being made by Busan city hall. The marine industry survey is the national approval statistics of the nation s first marine industry developed by Busan city hall and used as basic data for revitalizing Busan marine industry. The purpose of the marine industry survey is to understand the importance of the marine industry in the entire industry of Busan and to identify the most important factors in the development of the marine industry. As the types of statistical surveys targeting the recent business have diversified, the survey environment has become worse such as increased responsiveness of businesses, and the minimum wage has risen sharply, the cost of statistical surveys is increasing every year, and it is expected to face many difficulties in the promotion of statistical surveys in the future. In this study, we study the sampling method, extracted samples from stratified sampling method in the population in order to conduct an efficient statistical survey, get the sample by the stratified systematic sampling method in the population, compare the estimates obtained from the sample with the results of the previous surveys, and look into whether the sample survey can be switched.

Non-response problem is an issue of great concern to all the researchers because it pervades almost all survey research. This ultimately creates potential for bias. The higher the non-response rate the greater the bias if the characteristic under study in respondents differs markedly from non-respondents. This paper reviews and explores further the nature and properties of non-response weighting adjustment approach as applied to sample surveys as a means of handling non-coverage and unit non-response bias in survey estimates. Consequently, a non-response weighting scheme is herein developed. Not only the attitude of the interviewees, but also sample and survey design, fieldwork approach and characteristics of organization influence response results. This study encompasses the application of stratified random sampling because it is well known that stratification method minimizes the variance of the estimates through the process of dividing the population into groups (strata) which are more or less homogeneous. Thus, stratification increases the precision of the estimate. The emphasis of this paper is practical rather than theoretical. Hence the discussion is illustrated with real examples from surveys (in particular 2003 KDHS) conducted by Central Bureau of Statistics (CBS) - Kenya. Some suggestions are made for improving the quality of non-response weighting. Keywords: Survey non-response; non-response adjustment factors; weighting; sampling frame; stratified sampling > East African Journal of Statistics Vol. 1 (2) 2006: pp. 143-162

This book provides the reader with the basic skills and tools of statistics and probability in the context of engineering modeling and analysis. The emphasis is on the application and the reasoning be

Chapter 1 - Bioinformatics methods: Application toward analyses and interpretation of experimental data

In assembling our guidelines, we examined ideas in the area of population estimation and also in two areas related to population estimation: (1) sample (statistical) surveys; and (2) population forecasting. In regard to the two related fields, we found ideas that can be applied directly as guidelines for developing and presenting estimates and others that can be easily adapted for this purpose. While, as this book attests, there are substantial areas of overlap among sample surveys, population forecasting, and population estimation, there are important distinctions. And these distinctions lead to different guidelines.

This chapter introduces the basic definitions and methods of probability and statistical analysis, which are the foundation for all work reliability and fire risk analysis, and other topics of this section. With increased availability of sizeable quantities of reliable data on a whole range of topics related to fire protection engineering, it is essential that the analysis of this data be based on sound mathematical principles from probability and statistical theory. The chapter is divided into two main sections: probability theory, and statistics.

In sample surveys, stratified sampling is useful if the strata weights are known for each stratum. If they are not known double sampling may be used by selecting a large preliminary sample to estimate the strata weights. Then a stratified sample may be selected independently or from the initial sample. If the problem of non-response is also present then the strata are to be virtually divided into two disjoint and exhaustive groups of respondents and non-respondents. A subsamples from non-respondents is then selected and second more extensive attempt is to be group is to be made for obtaining the required information. The problem of obtaining a compromise allocation for first and second phase of sampling is the formulated as a multi-objective non- linear programming problem that minimizes the sum of variances of the stratified sample mean subject to the non-linear cost constraint. The formulated problem is solved using fuzzy programming and fuzzy goal programming based on piecewise linear approximation. A numerical example is presented to illustrate the computational details. Keywords: Non-response, Multivariate Stratified Sampling, Multiobjective Integer non-linear programming problem, Fuzzy Programming, Travel cost

Concerns about the cost-effectiveness of conservation monitoring prompt a reassessment of systematic aerial sample surveys, which have been widely applied to census wildlife and livestock in African savannas for more than 30 years. First, we use results from high-resolution sample surveys in Laikipia District (northern Kenya) to directly compare results from aerial total and sample surveys, showing few systematic differences in their estimates of wildlife abundance but great differences in cost and scope. Second, we quantify how the precision of population estimates is affected by survey resolution and species density. Results suggest that lower survey resolutions widely used in the past to census wildlife and livestock resources have been insufficient to reliably estimate all but the most abundant species. Third, we describe how sample survey data can be used to map the potential for human–wildlife conflict across large landscapes. High-resolution sample surveys in Laikipia have revealed causes and consequences of ecosystem change, advanced our understanding of ungulate population dynamics, guided wildlife management and conservation action, and increased confidence in sample survey methodology. However, further refinements in sample survey methods are needed to improve cost-effectiveness.

Calibration approach is widely used survey sampling that incorporates auxiliary information to increase the precision of survey estimates. In this manuscript, we propose two new calibration estimators of population mean in stratified sampling, using the known auxiliary information on mean and coefficient of variation in each stratum. A numerical example is presented to illustrate the application and computational details of the proposed calibration estimators. Moreover, a simulation study is carried out to compare the performance of the proposed calibration estimators.

Controlled Branching Processes