# Survey Sampling Theory and Applications

## 1st Edition

Authors:
Paperback ISBN: 9780128118481
eBook ISBN: 9780128118979
Published Date: 9th March 2017
Page Count: 930
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## Description

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. Many other books available for graduate students do not contain material on recent developments in the area of survey sampling.

The book covers a wide spectrum of topics on the subject, including repetitive sampling over two occasions with varying probabilities, ranked set sampling, Fays method for balanced repeated replications, mirror-match bootstrap, and controlled sampling procedures. Many topics discussed here are not available in other text books. In each section, theories are illustrated with numerical examples. At the end of each chapter theoretical as well as numerical exercises are given which can help graduate students.

## Key Features

• Covers a wide spectrum of topics on survey sampling and statistics
• Serves as an ideal text for graduate students and researchers in survey sampling theory and applications
• Contains material on recent developments in survey sampling not covered in other books
• Illustrates theories using numerical examples and exercises

Undergraduates and graduate students in statistics and mathematics; statisticians in Government and private sector organizations

Chapter 1. Preliminaries and Basics of Probability Sampling

• 1.1. Introduction
• 1.2. Definitions and Terminologies
• 1.3. Sampling Design and Inclusion Probabilities
• 1.4. Methods of Selection of Sample
• 1.5. Hanurav's Algorithm
• 1.6. Ordered and Unordered Sample
• 1.7. Data
• 1.8. Sampling From Hypothetical Populations
• 1.9. Exercises

Chapter 2. Unified Sampling Theory: Design-Based Inference

• 2.1. Introduction
• 2.2. Definitions and Terminologies
• 2.3. Linear Unbiased Estimators
• 2.4. Properties of the Horvitz–Thompson Estimator
• 2.5. Nonexistence Theorems
• 2.6. Admissible Estimators
• 2.7. Sufficiency in Finite Population
• 2.8. Sampling Strategies
• 2.9. Discussions
• 2.10. Exercises

Chapter 3. Simple Random Sampling

• 3.1. Introduction
• 3.2. Simple Random Sampling Without Replacement
• 3.3. Simple Random Sampling With Replacement
• 3.4. Interval Estimation
• 3.5. Determination of Sample Size
• 3.6. Inverse Sampling
• 3.7. Exercises

Chapter 4. Systematic Sampling

• 4.1. Introduction
• 4.2. Linear Systematic Sampling
• 4.3. Efficiency of Systematic Sampling
• 4.4. Linear Systematic Sampling Using Fractional Interval
• 4.5. Circular Systematic Sampling
• 4.6. Variance Estimation
• 4.7. Two-Dimensional Systematic Sampling
• 4.8. Exercises

Chapter 5. Unequal Probability Sampling

• 5.1. Introduction
• 5.2. Probability Proportional to Size With Replacement Sampling Scheme
• 5.3. Probability Proportional to Size Without Replacement Sampling Scheme
• 5.4. Inclusion Probability Proportional to Measure of Size Sampling Scheme
• 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

Chapter 6. Inference Under Superpopulation Model

• 6.1. Introduction
• 6.2. Definitions
• 6.3. Model-Assisted Inference
• 6.4. Model-Based Inference
• 6.5. Robustness of Designs and Predictors
• 6.6. Bayesian Inference
• 6.7. Comparison of Strategies Under Superpopulation Models
• 6.8. Discussions
• 6.9. Exercises

Chapter 7. Stratified Sampling

• 7.1. Introduction
• 7.2. Definition of Stratified Sampling
• 7.3. Advantages of Stratified Sampling
• 7.4. Estimation Procedure
• 7.5. Allocation of Sample Size
• 7.6. Comparison Between Stratified and Unstratified Sampling
• 7.7. Construction of Strata
• 7.8. Estimation of Gain Due To Stratification
• 7.9. Poststratification
• 7.10. Exercises

Chapter 8. Ratio Method of Estimation

• 8.1. Introduction
• 8.2. Ratio Estimator for Population Ratio
• 8.3. Ratio Estimator for Population Total
• 8.4. Biases and Mean-Square Errors for Specific Sampling Designs
• 8.5. Interval Estimation
• 8.6. Unbiased Ratio, Almost Unbiased Ratio, and Unbiased Ratio–Type Estimators
• 8.7. Ratio Estimator for Stratified Sampling
• 8.8. Ratio Estimator for Several Auxiliary Variables
• 8.9. Exercises

Chapter 9. Regression, Product, and Calibrated Methods of Estimation

• 9.1. Introduction
• 9.2. Difference Estimator
• 9.3. Regression Estimator
• 9.4. Product Method of Estimation
• 9.5. Comparison Between the Ratio, Regression, Product, and Conventional Estimators
• 9.6. Dual to Ratio Estimator
• 9.7. Calibration Estimators
• 9.8. Exercises
• Appendix 9A

Chapter 10. Two-Phase Sampling

• 10.1. Introduction
• 10.2. Two-Phase Sampling for Estimation
• 10.3. Two-Phase Sampling for Stratification
• 10.4. Two-Phase Sampling for Selection of Sample
• 10.5. Two-Phase Sampling for Stratification and Selection of Sample
• 10.6. Exercises

Chapter 11. Repetitive Sampling

• 11.1. Introduction
• 11.2. Estimation of Mean for the Most Recent Occasion
• 11.3. Estimation of Change Over Two Occasions
• 11.4. Estimation of Mean of Means
• 11.5. Exercises

Chapter 12. Cluster Sampling

• 12.1. Introduction
• 12.2. Estimation of Population Total and Variance
• 12.3. Efficiency of Cluster Sampling
• 12.4. Probability Proportional to Size With Replacement Sampling
• 12.5. Estimation of Mean per Unit
• 12.6. Exercises

Chapter 13. Multistage Sampling

• 13.1. Introduction
• 13.2. Two-Stage Sampling Scheme
• 13.3. Estimation of the Population Total and Variance
• 13.4. First-Stage Units Are Selected by PPSWR Sampling Scheme
• 13.5. Modification of Variance Estimators
• 13.6. More than Two-Stage Sampling
• 13.7. Estimation of Mean per Unit
• 13.8. Optimum Allocation
• 13.9. Self -weighting Design
• 13.10. Exercises

Chapter 14. Variance/Mean Square Estimation

• 14.1. Introduction
• 14.2. Linear Unbiased Estimators
• 14.3. Nonnegative Variance/Mean Square Estimation
• 14.4. Exercises

Chapter 15. Nonsampling Errors

• 15.1. Introduction
• 15.2. Sources of Nonsampling Errors
• 15.3. Controlling of Nonsampling Errors
• 15.4. Treatment of Nonresponse Error
• 15.5. Measurement Error
• 15.6. Exercises

Chapter 16. Randomized Response Techniques

• 16.1. Introduction
• 16.2. Randomized Response Techniques for Qualitative Characteristics
• 16.3. Extension to More than One Categories
• 16.4. Randomized Response Techniques for Quantitative Characteristics
• 16.5. General Method of Estimation
• 16.6. Optional Randomized Response Techniques
• 16.7. Measure of Protection of Privacy
• 16.8. Optimality Under Superpopulation Model
• 16.9. Exercises

Chapter 17. Domain and Small Area Estimation

• 17.1. Introduction
• 17.2. Domain Estimation
• 17.3. Small Area Estimation
• 17.4. Exercises

Chapter 18. Variance Estimation: Complex Survey Designs

• 18.1. Introduction
• 18.2. Linearization Method
• 18.3. Random Group Method
• 18.4. Jackknife Method
• 18.5. Balanced Repeated Replication Method
• 18.6. Bootstrap Method
• 18.7. Generalized Variance Functions
• 18.8. Comparison Between the Variance Estimators
• 18.9. Exercises

Chapter 19. Complex Surveys: Categorical Data Analysis

• 19.1. Introduction
• 19.2. Pearsonian Chi-Square Test for Goodness of Fit
• 19.3. Goodness of Fit for a General Sampling Design
• 19.4. Test of Independence
• 19.5. Tests of Homogeneity
• 19.6. Chi-Square Test Based on Superpopulation Model
• 19.7. Concluding Remarks
• 19.8. Exercises

Chapter 20. Complex Survey Design: Regression Analysis

• 20.1. Introduction
• 20.2. Design-Based Approach
• 20.3. Model-Based Approach
• 20.4. Concluding Remarks
• 20.5. Exercises

Chapter 21. Ranked Set Sampling

• 21.1. Introduction
• 21.2. Ranked Set Sampling by Simple Random Sampling With Replacement Method
• 21.3. Simple Random Sampling Without Replacement
• 21.4. Size-Biased Probability of Selection
• 21.5. Concluding Remarks
• 21.6. Exercises

Chapter 22. Estimating Functions

• 22.1. Introduction
• 22.2. Estimating Function and Estimating Equations
• 22.3. Estimating Function From Superpopulation Model
• 22.4. Estimating Function for a Survey Population
• 22.5. Interval Estimation
• 22.6. Nonresponse
• 22.7. Concluding Remarks
• 22.8. Exercises

Chapter 23. Estimation of Distribution Functions and Quantiles

• 23.1. Introduction
• 23.2. Estimation of Distribution Functions
• 23.3. Estimation of Quantiles
• 23.4. Estimation of Median
• 23.5. Confidence Interval for Distribution Function and Quantiles
• 23.6. Concluding Remarks
• 23.7. Exercises

Chapter 24. Controlled Sampling

• 24.1. Introduction
• 24.2. Pioneering Method
• 24.3. Experimental Design Configurations
• 24.4. Application of Linear Programming
• 24.5. Nearest Proportional to Size Design
• 24.6. Application of Nonlinear Programming
• 24.7. Coordination of Samples Overtime
• 24.8. Discussions
• 24.9. Exercises

Chapter 25. Empirical Likelihood Method in Survey Sampling

• 25.1. Introduction
• 25.2. Scale Load Approach
• 25.3. Empirical Likelihood Approach
• 25.4. Empirical Likelihood for Simple Random Sampling
• 25.5. Pseudo–empirical Likelihood Method
• 25.6. Asymptotic Behavior of MPEL Estimator
• 25.7. Empirical Likelihood for Stratified Sampling
• 25.8. Model-Calibrated Pseudoempirical Likelihood
• 25.9. Pseudo–empirical Likelihood to Raking
• 25.10. Empirical Likelihood Ratio Confidence Intervals
• 25.11. Concluding Remarks
• 25.12. Exercises

Chapter 26. Sampling Rare and Mobile Populations

• 26.1. Introduction
• 26.2. Screening
• 26.3. Disproportionate Sampling
• 26.4. Multiplicity or Network Sampling
• 26.5. Multiframe Sampling
• 26.6. Snowball Sampling
• 26.7. Location Sampling
• 26.8. Sequential Sampling
• 26.9. Adaptive Sampling
• 26.10. Capture–Recapture Method
• 26.11. Exercises

No. of pages:
930
Language:
English
Published:
9th March 2017
Imprint:
Paperback ISBN:
9780128118481
eBook ISBN:
9780128118979

## About the Author

### Raghunath Arnab

Prof. Raghunath Arnab is a Professor of Statistics, University of Botswana, Botswana and Honorary Professor of Statistics, University of KwaZulu-Natal, South Africa. Prof. Arnab received his Ph.D. degree in 1981 from the Indian Statistical Institute, Kolkata. He is a co-author of the book A new concept for tuning design weights in survey sampling (jointly with Prof. S. Singh, Prof. A. Sedory, Prof. M. der Mar Rueda, Prof. A. Arcos) and an author of numerous research articles, Associate editor of the Journal of Statistical Theory and Practice, Model Assisted statistics and its Applications, Journal of the Indian Society of Agricultural Statistics and Advances and Applications in Statistics. Prof. Arnab was an elected member of the International Statistical Institute, Life member of the International Statistical Institute and a member of the Biometric Society.

### Affiliations and Expertise

Department of Statistics, University of Botswana, Botswana, and University of Kwa-Zulu Natal, South Africa