Sampling Designs Dependent on Sample Parameters of Auxiliary Variables (SpringerBriefs in Statistics)

✍ Scribed by Janusz L. Wywiał

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 113
• Category: Library

✦ Synopsis

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

Preface
Contents
1 Introduction and Basic Sampling Strategies
1.1 Aim and Outline of This Book
1.2 Population and Parameters
1.3 Sampling Design and Sampling Scheme
1.4 Estimation
References
2 Sampling Designs Dependent on Sample Moments of Auxiliary Variables
2.1 Sampling Design Proportional to Sample Mean
2.2 Sampford's Sampling Design
2.3 Sampling Design Proportional to Sample Variance
2.4 Sampling Designs Proportional to the Generalized Variance
References
3 Sampling Designs Based on Order Statistics of an Auxiliary Variable
3.1 Basic Properties of Order Statistics
3.2 Sampling Design Proportional to Function of One-Order Statistic
3.3 Sampling Design Proportional to Function of Two-Order Statistics
3.4 Sampling Design Proportional to Function of Three-Order Statistics
References
4 Simulation Analysis of the Efficiency of the Strategies
4.1 Description of the Simulation Experiments
4.2 Efficiency of Estimation Strategies Dependent on Sample Moments or Order Statistics
4.3 Efficiency of Estimation Strategies Dependent on the Sum of Order Statistics
4.4 Efficiency Estimation of Domain Mean
4.5 Estimation of Quantiles
4.6 Conclusions
References
5 Sampling Designs Dependent on a Continuous Auxiliary Variable
5.1 Introduction
5.2 Basic Definitions and Theorems
5.3 The Inclusion Function Proportional to the Values of the Auxiliary Variable
5.4 Sampling Designs as a Function of an Order Statistic
5.4.1 General Results
5.4.2 Uniform Distribution
5.5 Accuracy Analysis
References