Survey sampling theory and applications / Raghunath Arnab.

Format:

Book

Author/Creator:

Raghunath, Arnab, author.

Language:

English

Subjects (All):

Sampling (Statistics).

Mathematical statistics.

Physical Description:

1 online resource (932 pages)

Edition:

1st ed.

Place of Publication:

London, England : Academic Press, 2017.

Summary:

Survey Sampling Theory and Applications offers a comprehensive overview of survey sampling, including the basics of sampling theory and practice, as well as research-based topics and examples of emerging trends.The text is useful for basic and advanced survey sampling courses.

Contents:

Front Cover

SURVEY SAMPLING THEORY AND APPLICATIONS

Copyright

Dedication

CONTENTS

PREFACE

DESCRIPTIONS OF CHAPTERS

ACKNOWLEDGMENTS

1 - Preliminaries and Basics of Probability Sampling

1.1 INTRODUCTION

1.2 DEFINITIONS AND TERMINOLOGIES

1.2.1 Population and Unit

1.2.2 Finite and Infinite Populations

1.2.3 Sampling Frame

1.2.4 Parameter and Parameter Space

1.2.5 Complete Enumeration and Sample Survey

1.2.6 Sampling and Nonsampling Errors

1.2.7 Sample

1.2.8 Probability and Purposive Sampling

1.3 SAMPLING DESIGN AND INCLUSION PROBABILITIES

1.3.1 Sampling Design

1.3.2 Inclusion Probabilities

1.3.3 Consistency Conditions of Inclusion Probabilities

1.3.4 Fixed Effective Size Design

1.3.5 Fixed Sample Size Design

1.4 METHODS OF SELECTION OF SAMPLE

1.4.1 Cumulative Total Method

1.4.2 Sampling Scheme

1.4.3 With and Without Replacement Sampling

1.4.4 Simple Random Sampling With Replacement

1.4.5 Simple Random Sampling Without Replacement

1.4.6 Probability Proportional to Size With Replacement Sampling

1.4.7 Probability Proportional to Size Without Replacement Sampling

1.4.8 Lahiri-Midzuno-Sen Sampling Scheme

1.5 HANURAV'S ALGORITHM

1.6 ORDERED AND UNORDERED SAMPLE

1.7 DATA

1.7.1 Sample Space

1.8 SAMPLING FROM HYPOTHETICAL POPULATIONS

1.8.1 Sampling From a Uniform Population

1.8.2 Sampling From a Normal Population

1.8.3 Sampling From a Binomial Population

1.9 EXERCISES

2 - Unified Sampling Theory: Design-Based Inference

2.1 INTRODUCTION

2.2 DEFINITIONS AND TERMINOLOGIES

2.2.1 Noninformative and Adaptive (Sequential) Sampling Designs

2.2.2 Estimator and Estimate

2.2.3 Unbiased Estimator

2.2.4 Mean Square Error and Variance.

2.2.5 Uniformly Minimum Variance Unbiased Estimator

2.3 LINEAR UNBIASED ESTIMATORS

2.3.1 Conditions of Unbiasedness

2.3.2 Horvitz-Thompson Estimator

2.3.3 Hansen-Hurwitz Estimator

2.3.4 Unbiased Ratio Estimator

2.3.5 Difference and Generalized Difference Estimator

2.4 PROPERTIES OF THE HORVITZ-THOMPSON ESTIMATOR

2.5 NONEXISTENCE THEOREMS

2.5.1 Unicluster Sampling Design

2.5.2 Class of Linear Homogeneous Unbiased Estimators

2.5.3 Optimality of the Horvitz-Thompson Estimator

2.5.4 Class of All Unbiased Estimators

2.5.5 Class of Linear Unbiased Estimators

2.6 ADMISSIBLE ESTIMATORS

2.7 SUFFICIENCY IN FINITE POPULATION

2.7.1 Sufficiency and Likelihood

2.7.2 Minimal Sufficient Statistic

2.7.3 Rao-Blackwellization

2.8 SAMPLING STRATEGIES

2.8.1 Unbiased Strategy

2.8.2 Uniformly Minimum Variance Unbiased Strategy

2.8.3 Admissible Strategies

2.8.4 Minimax Strategy

2.9 DISCUSSIONS

2.10 EXERCISES

3 - Simple Random Sampling

3.1 INTRODUCTION

3.2 SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT

3.2.1 Sampling Scheme

3.2.2 Estimation of Population Mean and Variance

3.2.3 Estimation of Population Covariance

3.2.4 Estimation of Population Proportion

3.2.5 Estimation of Domain Mean and Total

3.3 SIMPLE RANDOM SAMPLING WITH REPLACEMENT

3.3.1 Sampling Scheme

3.3.2 Estimation of the Population Mean and Variance

3.3.3 Estimation of Population Proportion

3.3.4 Rao-Blackwellization

3.4 INTERVAL ESTIMATION

3.4.1 Confidence Intervals for Mean and Proportion

3.4.1.1 Large Sample Size

3.4.1.2 Small Sample Size

3.5 DETERMINATION OF SAMPLE SIZE

3.5.1 Consideration of the Cost of a Survey

3.5.2 Consideration of the Efficiency of Estimators

3.5.2.1 Given Variance

3.5.2.2 Given Coefficient of Variation

3.5.2.3 Given Margin of Permissible Error.

3.5.3 Use of Chebyshev Inequality

3.6 INVERSE SAMPLING

3.6.1 Simple Random Sampling Without Replacement

3.6.2 Simple Random Sampling With Replacement

3.7 EXERCISES

4 - Systematic Sampling

4.1 INTRODUCTION

4.2 LINEAR SYSTEMATIC SAMPLING

4.2.1 Linear Systematic Sampling With N/n=k an Integer

4.2.2 Linear Systematic Sampling With N/n=k Not an Integer

4.2.3 Estimation of the Population Mean and Its Variance

4.2.4 Nonexistence of Unbiased Variance Estimator

4.3 EFFICIENCY OF SYSTEMATIC SAMPLING

4.3.1 Comparison With Simple Random Sampling

4.3.2 Comparison With Stratified Sampling

4.3.3 Random Arrangement of Units

4.3.4 Population With Linear Trend

4.3.4.1 End Corrections

4.3.4.2 Balanced Systematic Sampling

4.3.5 Population With Periodic Variation

4.3.6 Autocorrelated Population

4.4 LINEAR SYSTEMATIC SAMPLING USING FRACTIONAL INTERVAL

4.5 CIRCULAR SYSTEMATIC SAMPLING

4.5.1 Circular Systematic Sampling With k=N/n as an Integer

4.5.2 Circular Systematic Sampling With N/n is Not an Integer

4.6 VARIANCE ESTIMATION

4.6.1 Single Systematic Sample

4.6.1.1 Random Arrangements of Units

4.6.1.2 Stratified Sampling With One Unit Per Stratum

4.6.1.3 Presence of Linear Trend

4.6.1.4 Presence of Autocorrelation Between Successive Units

4.6.1.5 Splitting of a Systematic Sample

4.6.2 Several Systematic Samples

4.7 TWO-DIMENSIONAL SYSTEMATIC SAMPLING

4.8 EXERCISES

5 - Unequal Probability Sampling

5.1 INTRODUCTION

5.2 PROBABILITY PROPORTIONAL TO SIZE WITH REPLACEMENT SAMPLING SCHEME

5.2.1 Cumulative Total Method

5.2.2 Lahiri's Method

5.2.3 Hansen-Hurwitz Estimator and its Variance

5.2.4 Rao-Blackwellization

5.3 PROBABILITY PROPORTIONAL TO SIZE WITHOUT REPLACEMENT SAMPLING SCHEME

5.3.1 Raj's Estimator and its Variance

5.3.2 Rao-Blackwellization.

5.3.2.1 Murthy's Estimator

5.4 INCLUSION PROBABILITY PROPORTIONAL TO MEASURE OF SIZE SAMPLING SCHEME

5.4.1 Inclusion Probability Proportional to Measure of Size Sampling With n=2

5.4.1.1 Brewer's Sampling Scheme

5.4.1.2 Durbin's Sampling Scheme

5.4.1.3 Hanurav's Sampling Scheme

5.4.2 Inclusion Probability Proportional to Measure of Size Sampling with n 2

5.4.2.1 Lahiri-Midzuno-Sen Sampling Design

5.4.2.2 Probability Proportionate to Size Systematic Sampling Scheme

5.4.2.3 Sampford's Sampling Scheme

5.4.2.3.1 Comparison of Efficiency

5.4.2.4 Poisson (or Bernoulli) Sampling

5.4.2.5 Use of Combinatorics

5.4.2.6 The Nearest Proportional to Size Sampling

5.5 PROBABILITY PROPORTIONAL TO AGGREGATE SIZE WITHOUT REPLACEMENT

5.6 RAO-HARTLEY-COCHRAN SAMPLING SCHEME

5.7 COMPARISON OF UNEQUAL (VARYING) PROBABILITY SAMPLING DESIGNS

5.8 EXERCISES

6 - Inference Under Superpopulation Model

6.1 INTRODUCTION

6.2 DEFINITIONS

6.2.1 Sampling Strategy

6.2.2 Noninformative Sampling Design

6.2.3 Design-Unbiased (or p-Unbiased) Estimator

6.2.4 Model-Unbiased (or ξ-Unbiased) Estimator

6.2.5 Model Design-Unbiased (or pξ-Unbiased) Estimator

6.2.6 Design-Based Inference

6.2.7 Model-Based Inference

6.2.8 Model-Assisted Inference

6.2.9 Optimal Estimator

6.2.10 Optimal Strategy

6.3 MODEL-ASSISTED INFERENCE

6.3.1 Optimal Design-Unbiased Predictors

6.3.1.1 Product Measure Model

6.3.1.2 Equicorrelation Model

6.3.1.3 Transformation Model

6.3.2 Optimal Model Design-Unbiased Prediction

6.3.3 Exchangeable Model

6.3.4 Random Permutation Model

6.4 MODEL-BASED INFERENCE

6.4.1 Optimal Model-Unbiased Prediction

6.4.1.1 Product Measure Model

6.4.1.2 Transformation Model

6.4.1.3 Multiple Regression Model

6.5 ROBUSTNESS OF DESIGNS AND PREDICTORS.

6.5.1 Robustness of Predictors

6.5.2 Balanced Sampling Design

6.5.3 Polynomial Regression Model

6.5.4 Balanced Sample of Order k

6.5.5 Optimality of Balanced Sampling

6.6 BAYESIAN INFERENCE

6.6.1 Bayes Estimator

6.7 COMPARISON OF STRATEGIES UNDER SUPERPOPULATION MODELS

6.7.1 Hansen-Hurwitz Strategy With Others

6.7.2 Horvitz-Thompson and Rao-Hartley-Cochran Strategy

6.7.3 Horvitz-Thompson and Lahiri-Midzuno-Sen Strategy

6.7.4 Rao-Hartley-Cochran and Lahiri-Midzuno-Sen Strategy

6.8 DISCUSSIONS

6.9 EXERCISES

7 - Stratified Sampling

7.1 INTRODUCTION

7.2 DEFINITION OF STRATIFIED SAMPLING

7.3 ADVANTAGES OF STRATIFIED SAMPLING

7.4 ESTIMATION PROCEDURE

7.4.1 Estimation of Population Mean

7.4.1.1 Arbitrary Fixed Sample Size Design

7.4.1.2 Simple Random Sampling Without Replacement

7.4.1.3 Probability Proportional to Size With Replacement Sampling

7.4.1.4 Simple Random Sampling With Replacement

7.4.2 Estimation of Population Proportion

7.4.2.1 Simple Random Sampling Without Replacement

7.4.2.2 Simple Random Sampling With Replacement

7.4.3 Interval Estimation

7.5 ALLOCATION OF SAMPLE SIZE

7.5.1 Optimum Allocation for Fixed Cost

7.5.2 Optimum Allocation for Fixed Variance

7.5.3 Simple Random Sampling Without Replacement

7.5.4 Simple Random Sampling With Replacement

7.5.5 Probability Proportional to Size With Replacement Sampling

7.5.6 Neyman Optimum Allocation

7.5.7 Proportional Allocation

7.6 COMPARISON BETWEEN STRATIFIED AND UNSTRATIFIED SAMPLING

7.6.1 Simple Random Sampling Without Replacement

7.6.2 Probability Proportional to Size With Replacement Sampling

7.6.3 Inclusion Probability Proportional to Size Sampling Scheme

7.7 CONSTRUCTION OF STRATA

7.7.1 Optimum Points of Stratification

7.7.1.1 Proportional Allocation.

7.7.1.2 Optimum Allocation.

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed March 24, 2017).

Description based on publisher supplied metadata and other sources.

OCLC:

975271963