Table Of ContentSurvey Sampling
Survey Sampling
Arijit Chaudhuri
CRC Press
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Library of Congress Cataloging-in-Publication Data
Names: Chaudhuri, Arijit, 1940- author.
Title: Survey sampling / Arijit Chaudhuri.
Description: Boca Raton, FL : CRC Press, 2018. | Includes bibliographical
references and index.
Identifiers: LCCN 2018014313| ISBN 9781498774741 (hardback) | ISBN
9781315154688 (ebook)
Subjects: LCSH: Sampling (Statistics)
Classification: LCC QA276.6 .C429 2018 | DDC 519.5/2--dc23
LC record available at https://lccn.loc.gov/2018014313
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Dedication
To
Bulu and to the memory of
Late Professor V.P. Godambe
Contents
Acknowledgment xi
About the author xiii
Preface xv
My plea for this composition and my target readership xvii
Introduction xxi
Chapter 1: Certain Essential Preliminaries 1
1.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Concepts of Population, Sample, Survey, Census, Sampling:
Design and Schemes, Estimator and Strategy . . . . . . . . . 1
1.2 Properties of Estimators and Strategies; Different Inferen-
tial Approaches: Design-Based, Predictive, Super-Population
Model-Based, Model-Assisted and Bayesian . . . . . . . . . . 5
1.3 Sufficiency, Minimal Sufficiency and Bayesian Sufficiency . . 10
1.4 Classes of Estimators . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Godambe’s and Basu’s Theorems on Non-Existence of UMV
Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Hanurav’s (1966) and Hege’s (1965) Exceptions and Remedial
Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Chapter 2: Further Essentials for Unstratified Uni-Stage Cases 19
2.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Labels: Their Roles and Related Controversies . . . . . . . . 20
2.2 Minimaxity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Necessary and Sufficient Conditions for Existence of an Unbi-
ased Estimator for a Total and of a Variance Estimator . . . 23
2.4 Determination of Sample-Size . . . . . . . . . . . . . . . . . 24
2.5 Varying Probability Sampling Methods and Associated
Estimation Procedures . . . . . . . . . . . . . . . . . . . . . 27
Chapter 3: More in Design-Based Sampling 31
3.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
vii
viii Contents
3.1 Stratified Sampling and Other Sampling and Estimation
Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Replicated Sampling and Its Applications . . . . . . . . . . . 56
3.3 Controlled Sampling . . . . . . . . . . . . . . . . . . . . . . . 57
3.4 Multi-Phase Sampling: Ratio and Regression Estimation . . 60
3.5 Sampling on Successive Occasions and Panel Sampling . . . 63
3.6 Non-Sampling Error and Non-Response Error Problems:
Weighting Adjustments and Imputation Techniques . . . . . 66
Chapter 4: Super-Population Modeling and Its Various Uses 67
4.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Super-Population Modeling . . . . . . . . . . . . . . . . . . . 67
4.2 Linearization Technique . . . . . . . . . . . . . . . . . . . . . 76
4.3 Small Area Estimation . . . . . . . . . . . . . . . . . . . . . 77
4.4 Jack-Knife . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5 Bootstrap in Finite Population Sampling . . . . . . . . . . . 83
4.6 Balanced Repeated Replication (BRR) . . . . . . . . . . . . 93
4.7 Kriging or Spatial Prediction . . . . . . . . . . . . . . . . . . 96
4.8 Estimating Equations and Estimating Functions . . . . . . . 97
4.9 Basu’s (1971) Circus Example . . . . . . . . . . . . . . . . . 102
Chapter 5: Indirect Questioning in Sensitive Surveys 105
5.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.1 Randomized Response Techniques: General Sampling and
Simple Random Sampling with Replacement . . . . . . . . . 105
5.2 A Few Indirect Questioning Techniques Other than RRT’s . 123
5.3 Three More Indirect Questioning Techniques . . . . . . . . . 125
Chapter 6: Adaptive and Network Sampling 127
6.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.1 Adaptive Sampling . . . . . . . . . . . . . . . . . . . . . . . 127
6.2 Network Sampling . . . . . . . . . . . . . . . . . . . . . . . . 130
6.3 A Live Problem and Application . . . . . . . . . . . . . . . . 132
Chapter 7: Inadequate and Multiple Frames 137
7.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.1 Sampling from Inadequate Frames . . . . . . . . . . . . . . . 137
7.2 Sampling from Multiple Frames . . . . . . . . . . . . . . . . 141
7.3 Conditional Inference . . . . . . . . . . . . . . . . . . . . . . 142
Chapter 8: Analytic Studies 145
8.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.1 Analytic Studies, Tests of Goodness of Fit, Independence,
Homogeneity, Regression and Categorical Analysis . . . . . . 145
Contents ix
Chapter 9: Case Studies 147
9.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
9.1 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Chapter 10: Lessons and Exercises 159
10.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
10.1 Examples, Exercises and Riders with Complete and Hinted
Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Chapter 11: Reviews 185
11.0 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
11.1 Reviews of Various Sampling Schemes . . . . . . . . . . . . . 185
Chapter 12: An Appraisal 189
12.0 Epilogue.AnAppraisalofthePast,theCurrentandtheFuture
Possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
References 193
Index 211
