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A much-needed reference on survey sampling and its applications that presents the latest advances in the field
Seeking to show that sampling theory is a living discipline with a very broad scope, Sampling and Estimation from Finite Populations examines the modern development of the theory and the foundations of survey sampling. It offers readers a critical approach to the subject and discusses putting theory into practice. It also explores the treatment of non-sampling errors featuring a range of topics from the problems of coverage to the treatment of non-response. In addition, the book includes real examples, applications, and a large set of exercises with solutions.
The book begins with a look at the history of survey sampling. It then offers chapters on: population, sample, and estimation; simple and systematic designs; stratification; sampling with unequal probabilities; balanced sampling; cluster and two-stage sampling; and other topics on sampling, such as spatial sampling, coordination in repeated surveys, and multiple survey frames. The book also includes sections on: post-stratification and calibration on marginal totals; calibration estimation; estimation of complex parameters; variance estimation by linearization; and much more.
Sampling and Estimation from Finite Populations:
- Provides an up-to-date review of the theory of sampling
- Discusses the foundation of inference in survey sampling, in particular, the model-based and design-based frameworks
- Reviews the problems of application of the theory into practice
- Deals with the treatment of non-sampling errors
Sampling and Estimation from Finite Populations is an excellent book for methodologists and researchers in survey agencies and advanced undergraduate and graduate students in social science, statistics, and survey courses.
A much-needed reference on survey sampling and its applications that presents the latest advances in the field
Seeking to show that sampling theory is a living discipline with a very broad scope, Sampling and Estimation from Finite Populations examines the modern development of the theory and the foundations of survey sampling. It offers readers a critical approach to the subject and discusses putting theory into practice. It also explores the treatment of non-sampling errors featuring a range of topics from the problems of coverage to the treatment of non-response. In addition, the book includes real examples, applications, and a large set of exercises with solutions.
The book begins with a look at the history of survey sampling. It then offers chapters on: population, sample, and estimation; simple and systematic designs; stratification; sampling with unequal probabilities; balanced sampling; cluster and two-stage sampling; and other topics on sampling, such as spatial sampling, coordination in repeated surveys, and multiple survey frames. The book also includes sections on: post-stratification and calibration on marginal totals; calibration estimation; estimation of complex parameters; variance estimation by linearization; and much more.
Sampling and Estimation from Finite Populations:
- Provides an up-to-date review of the theory of sampling
- Discusses the foundation of inference in survey sampling, in particular, the model-based and design-based frameworks
- Reviews the problems of application of the theory into practice
- Deals with the treatment of non-sampling errors
Sampling and Estimation from Finite Populations is an excellent book for methodologists and researchers in survey agencies and advanced undergraduate and graduate students in social science, statistics, and survey courses.
YVES TILLÉ, PhD, is a Professor at the University of Neuchâtel (Université de Neuchâtel) in Neuchâtel, Switzerland.
List of Figures xiii
List of Tables xvii
List of Algorithms xix
Preface xxi
Preface to the First French Edition xxiii
Table of Notations xxv
1 A History of Ideas in Survey Sampling Theory 1
1.1 Introduction 1
1.2 Enumerative Statistics During the 19th Century 2
1.3 Controversy on the use of Partial Data 4
1.4 Development of a Survey Sampling Theory 5
1.5 The US Elections of 1936 6
1.6 The Statistical Theory of Survey Sampling 6
1.7 Modeling the Population 8
1.8 Attempt to a Synthesis 9
1.9 Auxiliary Information 9
1.10 Recent References and Development 10
2 Population, Sample, and Estimation 13
2.1 Population 13
2.2 Sample 14
2.3 Inclusion Probabilities 15
2.4 Parameter Estimation 17
2.5 Estimation of a Total 18
2.6 Estimation of a Mean 19
2.7 Variance of the Total Estimator 20
2.8 Sampling with Replacement 22
Exercises 24
3 Simple and Systematic Designs 27
3.1 Simple Random Sampling without Replacement with Fixed Sample Size 27
3.1.1 Sampling Design and Inclusion Probabilities 27
3.1.2 The Expansion Estimator and its Variance 28
3.1.3 Comment on the Variance-Covariance Matrix 31
3.2 Bernoulli Sampling 32
3.2.1 Sampling Design and Inclusion Probabilities 32
3.2.2 Estimation 34
3.3 Simple Random Sampling with Replacement 36
3.4 Comparison of the Designs with and Without Replacement 38
3.5 Sampling with Replacement and Retaining Distinct Units 38
3.5.1 Sample Size and Sampling Design 38
3.5.2 Inclusion Probabilities and Estimation 41
3.5.3 Comparison of the Estimators 44
3.6 Inverse Sampling with Replacement 45
3.7 Estimation of Other Functions of Interest 47
3.7.1 Estimation of a Count or a Proportion 47
3.7.2 Estimation of a Ratio 48
3.8 Determination of the Sample Size 50
3.9 Implementation of Simple Random Sampling Designs 51
3.9.1 Objectives and Principles 51
3.9.2 Bernoulli Sampling 51
3.9.3 Successive Drawing of the Units 52
3.9.4 Random Sorting Method 52
3.9.5 Selection-Rejection Method 53
3.9.6 The Reservoir Method 54
3.9.7 Implementation of Simple Random Sampling with Replacement 56
3.10 Systematic Sampling with Equal Probabilities 57
3.11 Entropy for Simple and Systematic Designs 58
3.11.1 Bernoulli Designs and Entropy 58
3.11.2 Entropy and Simple Random Sampling 60
3.11.3 General Remarks 61
Exercises 61
4 Stratification 65
4.1 Population and Strata 65
4.2 Sample, Inclusion Probabilities, and Estimation 66
4.3 Simple Stratified Designs 68
4.4 Stratified Design with Proportional Allocation 70
4.5 Optimal Stratified Design for the Total 71
4.6 Notes About Optimality in Stratification 74
4.7 Power Allocation 75
4.8 Optimality and Cost 76
4.9 Smallest Sample Size 76
4.10 Construction of the Strata 77
4.10.1 General Comments 77
4.10.2 Dividing a Quantitative Variable in Strata 77
4.11 Stratification Under Many Objectives 79
Exercises 80
5 Sampling with Unequal Probabilities 83
5.1 Auxiliary Variables and Inclusion Probabilities 83
5.2 Calculation of the Inclusion Probabilities 84
5.3 General Remarks 85
5.4 Sampling with Replacement with Unequal Inclusion Probabilities 86
5.5 Nonvalidity of the Generalization of the Successive Drawing without Replacement 88
5.6 Systematic Sampling with Unequal Probabilities 89
5.7 Deville's Systematic Sampling 91
5.8 Poisson Sampling 92
5.9 Maximum Entropy Design 95
5.10 Rao-Sampford Rejective Procedure 98
5.11 Order Sampling 100
5.12 Splitting Method 101
5.12.1 General Principles 101
5.12.2 Minimum Support Design 103
5.12.3 Decomposition into Simple Random Sampling Designs 104
5.12.4 Pivotal Method 107
5.12.5 Brewer Method 109
5.13 Choice of Method 110
5.14 Variance Approximation 111
5.15 Variance Estimation 114
Exercises 115
6 Balanced Sampling 119
6.1 Introduction 119
6.2 Balanced Sampling: Definition 120
6.3 Balanced Sampling and Linear Programming 122
6.4 Balanced Sampling by Systematic Sampling 123
6.5 Methode of Deville, Grosbras, and Roth 124
6.6 Cube Method 125
6.6.1 Representation of a Sampling Design in the form of a Cube 125
6.6.2 Constraint Subspace 126
6.6.3 Representation of the Rounding Problem 127
6.6.4 Principle of the Cube Method 130
6.6.5 The Flight Phase 130
6.6.6 Landing Phase by Linear Programming 133
6.6.7 Choice of the Cost Function 134
6.6.8 Landing Phase by Relaxing Variables 135
6.6.9 Quality of Balancing 135
6.6.10 An Example 136
6.7 Variance Approximation 137
6.8 Variance Estimation 140
6.9 Special Cases of Balanced Sampling 141
6.10 Practical Aspects of Balanced Sampling 141
Exercise 142
7 Cluster and Two-stage Sampling 143
7.1 Cluster Sampling 143
7.1.1 Notation and Definitions 143
7.1.2 Cluster Sampling with Equal Probabilities 146
7.1.3 Sampling Proportional to Size 147
7.2 Two-stage Sampling 148
7.2.1 Population, Primary, and Secondary Units 149
7.2.2 The Expansion Estimator and its Variance 151
7.2.3 Sampling with Equal Probability 155
7.2.4 Self-weighting Two-stage Design 156
7.3 Multi-stage Designs 157
7.4 Selecting Primary Units with Replacement 158
7.5 Two-phase Designs 161
7.5.1 Design and Estimation 161
7.5.2 Variance and Variance Estimation 162
7.6 Intersection of Two Independent Samples 163
Exercises 165
8 Other Topics on Sampling 167
8.1 Spatial Sampling 167
8.1.1 The Problem 167
8.1.2 Generalized Random Tessellation Stratified Sampling 167
8.1.3 Using the Traveling Salesman Method 169
8.1.4 The Local Pivotal Method 169
8.1.5 The Local Cube Method 169
8.1.6 Measures of Spread 170
8.2 Coordination in Repeated Surveys 172
8.2.1 The Problem 172
8.2.2 Population, Sample, and Sample Design 173
8.2.3 Sample Coordination and Response Burden 174
8.2.4 Poisson Method with Permanent Random Numbers 175
8.2.5 Kish and Scott Method for Stratified Samples 176
8.2.6 The Cotton and Hesse Method 176
8.2.7 The Rivière Method 177
8.2.8 The Netherlands Method 178
8.2.9 The Swiss Method 178
8.2.10 Coordinating Unequal Probability Designs with Fixed Size 181
8.2.11 Remarks 181
8.3 Multiple Survey Frames 182
8.3.1 Introduction 182
8.3.2 Calculating Inclusion Probabilities 183
8.3.3 Using Inclusion Probability Sums 184
8.3.4 Using a Multiplicity Variable 185
8.3.5 Using a Weighted Multiplicity Variable 186
8.3.6 Remarks 187
8.4 Indirect Sampling 187
8.4.1 Introduction 187
8.4.2 Adaptive Sampling 188
8.4.3 Snowball Sampling 188
8.4.4 Indirect Sampling 189
8.4.5 The Generalized Weight Sharing Method 190
8.5 Capture-Recapture 191
9 Estimation with a Quantitative Auxiliary Variable 195
9.1 The Problem 195
9.2 Ratio Estimator 196
9.2.1 Motivation and Definition 196
9.2.2 Approximate Bias of the Ratio Estimator 197
9.2.3 Approximate Variance of the Ratio Estimator 198
9.2.4 Bias Ratio 199
9.2.5 Ratio and Stratified Designs 199
9.3 The Difference Estimator 201
9.4 Estimation by Regression 202
9.5 The Optimal Regression Estimator 204
9.6 Discussion of the Three Estimation Methods 205
Exercises 208
10 Post-Stratification and Calibration on Marginal Totals 209
10.1 Introduction 209
10.2 Post-Stratification 209
10.2.1 Notation and Definitions 209
10.2.2 Post-Stratified Estimator 211
10.3 The Post-Stratified Estimator in Simple Designs 212
10.3.1 Estimator 212
10.3.2 Conditioning in a Simple Design 213
10.3.3 Properties of the Estimator in a Simple Design 214
10.4 Estimation by Calibration on Marginal Totals 217
10.4.1 The Problem 217
10.4.2 Calibration on Marginal Totals 218
10.4.3 Calibration and Kullback-Leibler Divergence 220
10.4.4 Raking Ratio Estimation 221
10.5 Example 221
Exercises 224
11 Multiple Regression Estimation 225
11.1 Introduction 225
11.2 Multiple Regression Estimator 226
11.3 Alternative Forms of the Estimator 227
11.3.1 Homogeneous Linear Estimator 227
11.3.2 Projective Form 228
11.3.3 Cosmetic Form 228
11.4 Calibration of the Multiple Regression Estimator 229
11.5 Variance of the Multiple Regression Estimator 230
11.6 Choice of Weights 231
11.7 Special Cases 231
11.7.1 Ratio Estimator 231
11.7.2 Post-stratified Estimator 231
11.7.3 Regression Estimation with a Single Explanatory Variable 233
11.7.4 Optimal Regression Estimator 233
11.7.5 Conditional Estimation 235
11.8 Extension to Regression Estimation 236
Exercise 236
12 Calibration Estimation 237
12.1 Calibrated Methods 237
12.2 Distances and Calibration Functions 239
12.2.1 The Linear Method 239
12.2.2 The Raking Ratio Method 240
12.2.3 Pseudo Empirical Likelihood 242
12.2.4 Reverse...
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: | Gebunden |
| ISBN-13: | 9780470682050 |
| ISBN-10: | 0470682051 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Tille, Yves |
| Hersteller: | Wiley |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 246 x 175 x 30 mm |
| Von/Mit: | Yves Tille |
| Erscheinungsdatum: | 07.04.2020 |
| Gewicht: | 0,93 kg |
YVES TILLÉ, PhD, is a Professor at the University of Neuchâtel (Université de Neuchâtel) in Neuchâtel, Switzerland.
List of Figures xiii
List of Tables xvii
List of Algorithms xix
Preface xxi
Preface to the First French Edition xxiii
Table of Notations xxv
1 A History of Ideas in Survey Sampling Theory 1
1.1 Introduction 1
1.2 Enumerative Statistics During the 19th Century 2
1.3 Controversy on the use of Partial Data 4
1.4 Development of a Survey Sampling Theory 5
1.5 The US Elections of 1936 6
1.6 The Statistical Theory of Survey Sampling 6
1.7 Modeling the Population 8
1.8 Attempt to a Synthesis 9
1.9 Auxiliary Information 9
1.10 Recent References and Development 10
2 Population, Sample, and Estimation 13
2.1 Population 13
2.2 Sample 14
2.3 Inclusion Probabilities 15
2.4 Parameter Estimation 17
2.5 Estimation of a Total 18
2.6 Estimation of a Mean 19
2.7 Variance of the Total Estimator 20
2.8 Sampling with Replacement 22
Exercises 24
3 Simple and Systematic Designs 27
3.1 Simple Random Sampling without Replacement with Fixed Sample Size 27
3.1.1 Sampling Design and Inclusion Probabilities 27
3.1.2 The Expansion Estimator and its Variance 28
3.1.3 Comment on the Variance-Covariance Matrix 31
3.2 Bernoulli Sampling 32
3.2.1 Sampling Design and Inclusion Probabilities 32
3.2.2 Estimation 34
3.3 Simple Random Sampling with Replacement 36
3.4 Comparison of the Designs with and Without Replacement 38
3.5 Sampling with Replacement and Retaining Distinct Units 38
3.5.1 Sample Size and Sampling Design 38
3.5.2 Inclusion Probabilities and Estimation 41
3.5.3 Comparison of the Estimators 44
3.6 Inverse Sampling with Replacement 45
3.7 Estimation of Other Functions of Interest 47
3.7.1 Estimation of a Count or a Proportion 47
3.7.2 Estimation of a Ratio 48
3.8 Determination of the Sample Size 50
3.9 Implementation of Simple Random Sampling Designs 51
3.9.1 Objectives and Principles 51
3.9.2 Bernoulli Sampling 51
3.9.3 Successive Drawing of the Units 52
3.9.4 Random Sorting Method 52
3.9.5 Selection-Rejection Method 53
3.9.6 The Reservoir Method 54
3.9.7 Implementation of Simple Random Sampling with Replacement 56
3.10 Systematic Sampling with Equal Probabilities 57
3.11 Entropy for Simple and Systematic Designs 58
3.11.1 Bernoulli Designs and Entropy 58
3.11.2 Entropy and Simple Random Sampling 60
3.11.3 General Remarks 61
Exercises 61
4 Stratification 65
4.1 Population and Strata 65
4.2 Sample, Inclusion Probabilities, and Estimation 66
4.3 Simple Stratified Designs 68
4.4 Stratified Design with Proportional Allocation 70
4.5 Optimal Stratified Design for the Total 71
4.6 Notes About Optimality in Stratification 74
4.7 Power Allocation 75
4.8 Optimality and Cost 76
4.9 Smallest Sample Size 76
4.10 Construction of the Strata 77
4.10.1 General Comments 77
4.10.2 Dividing a Quantitative Variable in Strata 77
4.11 Stratification Under Many Objectives 79
Exercises 80
5 Sampling with Unequal Probabilities 83
5.1 Auxiliary Variables and Inclusion Probabilities 83
5.2 Calculation of the Inclusion Probabilities 84
5.3 General Remarks 85
5.4 Sampling with Replacement with Unequal Inclusion Probabilities 86
5.5 Nonvalidity of the Generalization of the Successive Drawing without Replacement 88
5.6 Systematic Sampling with Unequal Probabilities 89
5.7 Deville's Systematic Sampling 91
5.8 Poisson Sampling 92
5.9 Maximum Entropy Design 95
5.10 Rao-Sampford Rejective Procedure 98
5.11 Order Sampling 100
5.12 Splitting Method 101
5.12.1 General Principles 101
5.12.2 Minimum Support Design 103
5.12.3 Decomposition into Simple Random Sampling Designs 104
5.12.4 Pivotal Method 107
5.12.5 Brewer Method 109
5.13 Choice of Method 110
5.14 Variance Approximation 111
5.15 Variance Estimation 114
Exercises 115
6 Balanced Sampling 119
6.1 Introduction 119
6.2 Balanced Sampling: Definition 120
6.3 Balanced Sampling and Linear Programming 122
6.4 Balanced Sampling by Systematic Sampling 123
6.5 Methode of Deville, Grosbras, and Roth 124
6.6 Cube Method 125
6.6.1 Representation of a Sampling Design in the form of a Cube 125
6.6.2 Constraint Subspace 126
6.6.3 Representation of the Rounding Problem 127
6.6.4 Principle of the Cube Method 130
6.6.5 The Flight Phase 130
6.6.6 Landing Phase by Linear Programming 133
6.6.7 Choice of the Cost Function 134
6.6.8 Landing Phase by Relaxing Variables 135
6.6.9 Quality of Balancing 135
6.6.10 An Example 136
6.7 Variance Approximation 137
6.8 Variance Estimation 140
6.9 Special Cases of Balanced Sampling 141
6.10 Practical Aspects of Balanced Sampling 141
Exercise 142
7 Cluster and Two-stage Sampling 143
7.1 Cluster Sampling 143
7.1.1 Notation and Definitions 143
7.1.2 Cluster Sampling with Equal Probabilities 146
7.1.3 Sampling Proportional to Size 147
7.2 Two-stage Sampling 148
7.2.1 Population, Primary, and Secondary Units 149
7.2.2 The Expansion Estimator and its Variance 151
7.2.3 Sampling with Equal Probability 155
7.2.4 Self-weighting Two-stage Design 156
7.3 Multi-stage Designs 157
7.4 Selecting Primary Units with Replacement 158
7.5 Two-phase Designs 161
7.5.1 Design and Estimation 161
7.5.2 Variance and Variance Estimation 162
7.6 Intersection of Two Independent Samples 163
Exercises 165
8 Other Topics on Sampling 167
8.1 Spatial Sampling 167
8.1.1 The Problem 167
8.1.2 Generalized Random Tessellation Stratified Sampling 167
8.1.3 Using the Traveling Salesman Method 169
8.1.4 The Local Pivotal Method 169
8.1.5 The Local Cube Method 169
8.1.6 Measures of Spread 170
8.2 Coordination in Repeated Surveys 172
8.2.1 The Problem 172
8.2.2 Population, Sample, and Sample Design 173
8.2.3 Sample Coordination and Response Burden 174
8.2.4 Poisson Method with Permanent Random Numbers 175
8.2.5 Kish and Scott Method for Stratified Samples 176
8.2.6 The Cotton and Hesse Method 176
8.2.7 The Rivière Method 177
8.2.8 The Netherlands Method 178
8.2.9 The Swiss Method 178
8.2.10 Coordinating Unequal Probability Designs with Fixed Size 181
8.2.11 Remarks 181
8.3 Multiple Survey Frames 182
8.3.1 Introduction 182
8.3.2 Calculating Inclusion Probabilities 183
8.3.3 Using Inclusion Probability Sums 184
8.3.4 Using a Multiplicity Variable 185
8.3.5 Using a Weighted Multiplicity Variable 186
8.3.6 Remarks 187
8.4 Indirect Sampling 187
8.4.1 Introduction 187
8.4.2 Adaptive Sampling 188
8.4.3 Snowball Sampling 188
8.4.4 Indirect Sampling 189
8.4.5 The Generalized Weight Sharing Method 190
8.5 Capture-Recapture 191
9 Estimation with a Quantitative Auxiliary Variable 195
9.1 The Problem 195
9.2 Ratio Estimator 196
9.2.1 Motivation and Definition 196
9.2.2 Approximate Bias of the Ratio Estimator 197
9.2.3 Approximate Variance of the Ratio Estimator 198
9.2.4 Bias Ratio 199
9.2.5 Ratio and Stratified Designs 199
9.3 The Difference Estimator 201
9.4 Estimation by Regression 202
9.5 The Optimal Regression Estimator 204
9.6 Discussion of the Three Estimation Methods 205
Exercises 208
10 Post-Stratification and Calibration on Marginal Totals 209
10.1 Introduction 209
10.2 Post-Stratification 209
10.2.1 Notation and Definitions 209
10.2.2 Post-Stratified Estimator 211
10.3 The Post-Stratified Estimator in Simple Designs 212
10.3.1 Estimator 212
10.3.2 Conditioning in a Simple Design 213
10.3.3 Properties of the Estimator in a Simple Design 214
10.4 Estimation by Calibration on Marginal Totals 217
10.4.1 The Problem 217
10.4.2 Calibration on Marginal Totals 218
10.4.3 Calibration and Kullback-Leibler Divergence 220
10.4.4 Raking Ratio Estimation 221
10.5 Example 221
Exercises 224
11 Multiple Regression Estimation 225
11.1 Introduction 225
11.2 Multiple Regression Estimator 226
11.3 Alternative Forms of the Estimator 227
11.3.1 Homogeneous Linear Estimator 227
11.3.2 Projective Form 228
11.3.3 Cosmetic Form 228
11.4 Calibration of the Multiple Regression Estimator 229
11.5 Variance of the Multiple Regression Estimator 230
11.6 Choice of Weights 231
11.7 Special Cases 231
11.7.1 Ratio Estimator 231
11.7.2 Post-stratified Estimator 231
11.7.3 Regression Estimation with a Single Explanatory Variable 233
11.7.4 Optimal Regression Estimator 233
11.7.5 Conditional Estimation 235
11.8 Extension to Regression Estimation 236
Exercise 236
12 Calibration Estimation 237
12.1 Calibrated Methods 237
12.2 Distances and Calibration Functions 239
12.2.1 The Linear Method 239
12.2.2 The Raking Ratio Method 240
12.2.3 Pseudo Empirical Likelihood 242
12.2.4 Reverse...
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: | Gebunden |
| ISBN-13: | 9780470682050 |
| ISBN-10: | 0470682051 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Tille, Yves |
| Hersteller: | Wiley |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 246 x 175 x 30 mm |
| Von/Mit: | Yves Tille |
| Erscheinungsdatum: | 07.04.2020 |
| Gewicht: | 0,93 kg |
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