Model Assisted Survey Sampling

ISBN-13: 9780387406206 / Angielski / Miękka / 2003 / 695 str.

Bengt Swensson; Jan Wretman; Carl-Erik Sarndal

Opis

Now available in paperback. This book provides a comprehensive account of survey sampling theory and methodology which will be suitable for students and researchers across a variety of disciplines. A central theme is to show how statistical modeling is a vital component of the sampling process and in the choice of estimation technique. Statistical modeling has strongly influenced sampling theory in recent years and has clarified many issues related to the uses of auxiliary information in surveys. This is the first textbook that systematically extends traditional sampling theory with the aid of a modern model assisted outlook. The central ideas of sampling theory are developed from the unifying perspective of unequal probability sampling. The book covers classical topics as well as areas where significant new developments have taken place notably domain estimation, variance estimation, methods for handling nonresponse, models for measurement error, and the analysis of survey data. The authors have taken care to presuppose nothing more on the part of the reader than a first course in statistical inference and regression analysis. Throughout, the emphasis is on statistical ideas rather than advanced mathematics. Each chapter concludes with a range of exercises incorporating the analysis of data from actual finite populations. As a result, all those concerned with survey methodology or engaged in survey sampling will find this an invaluable and up-to-date coverage of the subject.

Recenzje

"I would recommend that this book be in the office of every survey methodologist."
(Journal of Official Statistics)

Spis treści

I Principles of Estimation for Finite Populations and Important Sampling Designs.- 1 Survey Sampling in Theory and Practice.- 1.1 Surveys in Society.- 1.2 Skeleton Outline of a Survey.- 1.3 Probability Sampling.- 1.4 Sampling Frame.- 1.5 Area Frames and Similar Devices.- 1.6 Target Population and Frame Population.- 1.7 Survey Operations and Associated Sources of Error.- 1.8 Planning a Survey and the Need for Total Survey Design.- 1.9 Total Survey Design.- 1.10 The Role of Statistical Theory in Survey Sampling.- Exercises.- 2 Basic Ideas in Estimation from Probability Samples.- 2.1 Introduction.- 2.2 Population, Sample, and Sample Selection.- 2.3 Sampling Design.- 2.4 Inclusion Probabilities.- 2.5 The Notion of a Statistic.- 2.6 The Sample Membership Indicators.- 2.7 Estimators and Their Basic Statistical Properties.- 2.8 The ? Estimator and Its Properties.- 2.9 With-Replacement Sampling.- 2.10 The Design Effect.- 2.11 Confidence Intervals.- Exercises.- 3 Unbiased Estimation for Element Sampling Designs.- 3.1 Introduction.- 3.2 Bernoulli Sampling.- 3.3 Simple Random Sampling.- 3.3.1 Simple Random Sampling without Replacement.- 3.3.2 Simple Random Sampling with Replacement.- 3.4 Systematic Sampling.- 3.4.1 Definitions and Main Result.- 3.4.2 Controlling the Sample Size.- 3.4.3 The Efficiency of Systematic Sampling.- 3.4.4 Estimating the Variance.- 3.5 Poisson Sampling.- 3.6 Probability Proportional-to-Size Sampling.- 3.6.1 Introduction.- 3.6.2 ?ps Sampling.- 3.6.3 pps Sampling.- 3.6.4 Selection from Randomly Formed Groups.- 3.7 Stratified Sampling.- 3.7.1 Introduction.- 3.7.2 Notation, Definitions, and Estimation.- 3.7.3 Optimum Sample Allocation.- 3.7.4 Alternative Allocations under STSI Sampling.- 3.8 Sampling without Replacement versus Sampling with Replacement.- 3.8.1 Alternative Estimators for Simple Random Sampling with Replacement.- 3.8.2 The Design Effect of Simple Random Sampling with Replacement.- Exercises.- 4 Unbiased Estimation for Cluster Sampling and Sampling in Two or More Stages.- 4.1 Introduction.- 4.2 Single-Stage Cluster Sampling.- 4.2.1 Introduction.- 4.2.2 Simple Random Cluster Sampling.- 4.3 Two-Stage Sampling.- 4.3.1 Introduction.- 4.3.2 Two-Stage Element Sampling.- 4.4 Multistage Sampling.- 4.4.1 Introduction and a General Result.- 4.4.2 Three-Stage Element Sampling.- 4.5 With-Replacement Sampling of PSUs.- 4.6 Comparing Simplified Variance Estimators in Multistage Sampling.- Exercises.- 5 Introduction to More Complex Estimation Problems.- 5.1 Introduction.- 5.2 The Effect of Bias on Confidence Statements.- 5.3 Consistency and Asymptotic Unbiasedness.- 5.4 ? Estimators for Several Variables of Study.- 5.5 The Taylor Linearization Technique for Variance Estimation.- 5.6 Estimation of a Ratio.- 5.7 Estimation of a Population Mean.- 5.8 Estimation of a Domain Mean.- 5.9 Estimation of Variances and Covariances in a Finite Population.- 5.10 Estimation of Regression Coefficients.- 5.10.1 The Parameters of Interest.- 5.10.2 Estimation of the Regression Coefficients.- 5.11 Estimation of a Population Median.- 5.12 Demonstration of Result 5.10.1.- Exercises.- II Estimation through Linear Modeling, Using Auxiliary Variables.- 6 The Regression Estimator.- 6.1 Introduction.- 6.2 Auxiliary Variables.- 6.3 The Difference Estimator.- 6.4 Introducing the Regression Estimator.- 6.5 Alternative Expressions for the Regression Estimator.- 6.6 The Variance of the Regression Estimator.- 6.7 Comments on the Role of the Model.- 6.8 Optimal Coefficients for the Difference Estimator.- Exercises.- 7 Regression Estimators for Element Sampling Designs.- 7.1 Introduction.- 7.2 Preliminary Considerations.- 7.3 The Common Ratio Model and the Ratio Estimator.- 7.3.1 The Ratio Estimator under SI Sampling.- 7.3.2 The Ratio Estimator under Other Designs.- 7.3.3 Optimal Sampling Design for the ? Weighted Ratio Estimator.- 7.3.4 Alternative Ratio Models.- 7.4 The Common Mean Model.- 7.5 Models Involving Population Groups.- 7.6 The Group Mean Model and the Poststratified Estimator.- 7.7 The Group Ratio Model and the Separate Ratio Estimator.- 7.8 Simple Regression Models and Simple Regression Estimators.- 7.9 Estimators Based on Multiple Regression Models.- 7.9.1 Multiple Regression Models.- 7.9.2 Analysis of Variance Models.- 7.10 Conditional Confidence Intervals.- 7.10.1 Conditional Analysis for BE Sampling.- 7.10.2 Conditional Analysis for the Poststratification Estimator.- 7.11 Regression Estimators for Variable-Size Sampling Designs.- 7.12 A Class of Regression Estimators.- 7.13 Regression Estimation of a Ratio of Population Totals.- Exercises.- 8 Regression Estimators for Cluster Sampling and Two-Stage Sampling.- 8.1 Introduction.- 8.2 The Nature of the Auxiliary Information When Clusters of Elements Are Selected.- 8.3 Comments on Variance and Variance Estimation in Two-Stage Sampling.- 8.4 Regression Estimators Arising Out of Modeling at the Cluster Level.- 8.5 The Common Ratio Model for Cluster Totals.- 8.6 Estimation of the Population Mean When Clusters Are Sampled.- 8.7 Design Effects for Single-Stage Cluster Sampling.- 8.8 Stratified Clusters and Poststratified Clusters.- 8.9 Regression Estimators Arising Out of Modeling at the Element Level.- 8.10 Ratio Models for Elements.- 8.11 The Group Ratio Model for Elements.- 8.12 The Ratio Model Applied within a Single PSU.- Exercises.- III Further Questions in Design and Analysis of Surveys.- 9 Two-Phase Sampling.- 9.1 Introduction.- 9.2 Notation and Choice of Estimator.- 9.3 The ?* Estimator.- 9.4 Two-Phase Sampling for Stratification.- 9.5 Auxiliary Variables for Selection in Two Phases.- 9.6 Difference Estimators.- 9.7 Regression Estimators for Two-Phase Sampling.- 9.8 Stratified Bernoulli Sampling in Phase Two.- 9.9 Sampling on Two Occasions.- 9.9.1 Estimating the Current Total.- 9.9.2 Estimating the Previous Total.- 9.9.3 Estimating the Absolute Change and the Sum of the Totals.- Exercises.- 10 Estimation for Domains.- 10.1 Introduction.- 10.2 The Background for Domain Estimation.- 10.3 The Basic Estimation Methods for Domains.- 10.4 Conditioning on the Domain Sample Size.- 10.5 Regression Estimators for Domains.- 10.6 A Ratio Model for Each Domain.- 10.7 Group Models for Domains.- 10.8 Problems Arising for Small Domains; Synthetic Estimation.- 10.9 More on the Comparison of Two Domains.- Exercises.- 11 Variance Estimation.- 11.1 Introduction.- 11.2 A Simplified Variance Estimator under Sampling without Replacement.- 11.3 The Random Groups Technique.- 11.3.1 Independent Random Groups.- 11.3.2 Dependent Random Groups.- 11.4 Balanced Half-Samples.- 11.5 The Jackknife Technique.- 11.6 The Bootstrap.- 11.7 Concluding Remarks.- Exercises.- 12 Searching for Optimal Sampling Designs.- 12.1 Introduction.- 12.2 Model-Based Optimal Design for the General Regression Estimator.- 12.3 Model-Based Optimal Design for the Group Mean Model.- 12.4 Model-Based Stratified Sampling.- 12.5 Applications of Model-Based Stratification.- 12.6 Other Approaches to Efficient Stratification.- 12.7 Allocation Problems in Stratified Random Sampling.- 12.8 Allocation Problems in Two-Stage Sampling.- 12.8.1 The ? Estimator of the Population Total.- 12.8.2 Estimation of the Population Mean.- 12.9 Allocation in Two-Phase Sampling for Stratification.- 12.10 A Further Comment on Mathematical Programming.- 12.11 Sampling Design and Experimental Design.- Exercises.- 13 Further Statistical Techniques for Survey Data.- 13.1 Introduction.- 13.2 Finite Population Parameters in Multivariate Regression and Correlation Analysis.- 13.3 The Effect of Sampling Design on a Statistical Analysis.- 13.4 Variances and Estimated Variances for Complex Analyses.- 13.5 Analysis of Categorical Data for Finite Populations.- 13.5.1 Test of Homogeneity for Two Populations.- 13.5.2 Testing Homogeneity for More than Two Finite Populations.- 13.5.3 Discussion of Categorical Data Tests for Finite Populations.- 13.6 Types of Inference When a Finite Population Is Sampled.- Exercises.- IV A Broader View of Errors in Surveys.- 14 Nonsampling Errors and Extensions of Probability Sampling Theory.- 14.1 Introduction.- 14.2 Historic Notes: The Evolution ofthe Probability Sampling Approach.- 14.3 Measurable Sampling Designs.- 14.4 Some Nonprobability Sampling Methods.- 14.5 Model-Based Inference from Survey Samples.- 14.6 Imperfections in the Survey Operations.- 14.6.1 Ideal Conditions for the Probability Sampling Approach.- 14.6.2 Extension of the Probability Sampling Approach.- 14.7 Sampling Frames.- 14.7.1 Frame Imperfections.- 14.7.2 Estimation in the Presence of Frame Imperfections.- 14.7.3 Multiple Frames.- 14.7.4 Frame Construction and Maintenance.- 14.8 Measurement and Data Collection.- 14.9 Data Processing.- 14.10 Nonresponse.- Exercises.- 15 Nonresponse.- 15.1 Introduction.- 15.2 Characteristics of Nonresponse.- 15.2.1 Definition of Nonresponse.- 15.2.2 Response Sets.- 15.2.3 Lack of Unbiased Estimators.- 15.3 Measuring Nonresponse.- 15.4 Dealing with Nonresponse.- 15.4.1 Planning of the Survey.- 15.4.2 Callbacks and Follow-Ups.- 15.4.3 Subsampling of Nonrespondents.- 15.4.4 Randomized Response.- 15.5 Perspectives on Nonresponse.- 15.6 Estimation in the Presence of Unit Nonresponse.- 15.6.1 Response Modeling.- 15.6.2 A Useful Response Model.- 15.6.3 Estimators That Use Weighting Only.- 15.6.4 Estimators That Use Weighting as Well as Auxiliary Variables.- 15.7 Imputation.- Exercises.- 16 Measurement Errors.- 16.1 Introduction.- 16.2 On the Nature of Measurement Errors.- 16.3 The Simple Measurement Model.- 16.4 Decomposition of the Mean Square Error.- 16.5 The Risk of Underestimating the Total Variance.- 16.6 Repeated Measurements as a Tool in Variance Estimation.- 16.7 Measurement Models Taking Interviewer Effects into Account.- 16.8 Deterministic Assignment of Interviewers.- 16.9 Random Assignment of Interviewers to Groups.- 16.10 Interpenetrating Subsamples.- 16.11 A Measurement Model with Sample-Dependent Moments.- Exercises.- 17 Quality Declarations for Survey Data.- 17.1 Introduction.- 17.2 Policies Concerning Information on Data Quality.- 17.3 Statistics Canada’s Policy on Informing Users of Data Quality and Methodology.- Exercise.- Appendix A Principles of Notation.- Appendix B The MU284 Population.- Appendix C The Clustered MU284 Population.- Appendix D The CO124 Population.- References.- Answers to Selected Exercises.- Author Index.