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2021 | Book

Introduction and Basic Sampling Strategies Read chapter Read first chapter

Sampling Designs Dependent on Sample Parameters of Auxiliary Variables

Author: Janusz L. Wywiał

Publisher: Springer Berlin Heidelberg

Book Series : SpringerBriefs in Statistics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This short monograph provides a synthesis of new research on sampling designs that are dependent on sample moments or the order statistics of auxiliary variables. The range of survey sampling methods and their applications has gradually increased over time, and these applications have led to new theoretical solutions that provide better sampling designs or estimators. Recently, several important properties of sampling designs have been discovered, and many new methods have been published. Offering an overview of these developments, this book describes sampling designs dependent on the sample generalized variance of auxiliary variables, examines properties of sampling designs proportional to functions of sample order statistics of the auxiliary variable, and takes into account continuous sampling designs. The text will be useful for students and statisticians whose work involves survey sampling, and it will inspire those looking for new sampling designs dependent on auxiliary variables.

Table of Contents

Frontmatter
Chapter 1. Introduction and Basic Sampling Strategies
Abstract
This chapter provides an introduction to the problem of using auxiliary variables to support the estimation of the mean in finite and fixed populations. The basic definitions connected with sampling design are presented and properties of the well-known ratio, regression, and Horvitz–Thompson-type estimators are considered.
Janusz L. Wywiał
Chapter 2. Sampling Designs Dependent on Sample Moments of Auxiliary Variables
Abstract
This chapter describes the properties of ratio-type estimators from a sample drawn according to sampling design proportional to a sample mean of an auxiliary variable. The next sampling design proportional to the sample variance of an auxiliary variable is considered as a particular case of a sampling design dependent on the sample generalized variance of a multivariate auxiliary variable. Properties of regression-type estimators under this sampling design are also considered. The well-known Sampford sampling design is taken into account as a sampling design with inclusion probabilities proportional to the auxiliary variable values.
Janusz L. Wywiał
Chapter 3. Sampling Designs Based on Order Statistics of an Auxiliary Variable
Abstract
In this chapter, the properties of sampling designs proportional to the sample order statistic (quantile) as well as functions of two- or three-order statistics are considered in detail. Conditional sampling designs are also taken into account and exact expressions for inclusion probabilities are presented. The sampling schemes for these sampling designs are also proposed, some of which are generalized to the case of continuous-type sampling designs in the last chapter of the book.
Janusz L. Wywiał
Chapter 4. Simulation Analysis of the Efficiency of the Strategies
Abstract
This chapter compares the accuracy of estimation of the population mean using Monte Carlo simulation studies. Several sampling strategies are considered which are treated as pairs consisting of estimators and sampling plans. In particular, the accuracy of conditional sampling designs is studied. Problems of estimation of domain means are treated separately. Moreover, the accuracy of quantile estimators from sampling designs dependent on order statistics is also considered.
Janusz L. Wywiał
Chapter 5. Sampling Designs Dependent on a Continuous Auxiliary Variable
Abstract
In contrast to the previous chapters, this chapter concerns the estimation of the continuous variable expected value of the variable under study, supported by a continuous auxiliary variable whose density function is known. Continuous versions of the definition of a sampling design and scheme are presented. In this context, the properties of the well-known Horvitz–Thompson statistic are considered. The two-dimensional gamma distribution of the variable under study and the auxiliary variable are taken into account. The mean of the variable under study is estimated by means of a ratio-type estimator. A continuous sampling design dependent on the order statistic of the uniformly distributed auxiliary variable is proposed and its inclusion functions are derived. Finally, this sampling design is used to estimate the mean. The accuracy of this estimation is studied in the case of the continuous joint distribution of the variable under study and the auxiliary variable.
Janusz L. Wywiał
Metadata
Title
Sampling Designs Dependent on Sample Parameters of Auxiliary Variables
Author
Janusz L. Wywiał
Copyright Year
2021
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-662-63413-4
Print ISBN
978-3-662-63412-7
DOI
https://doi.org/10.1007/978-3-662-63413-4

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