抽样理论与方法 英文版PDF电子书下载

1 PRELIMINARIES 1

1.1 Introduction 1

1.2 A Brief History of Survey Sampling 1

1.3 Sampling Designs and an Overview of Sampling 3

1.4 Ingredients of a Survey 3

1.5 Probability Sampling 4

1.6 Precision and Confidence Intervals 5

1.7 Biased Estimators 5

1.8 The Mean-Squared Error 6

1.9 Unbiased Estimation 7

PROBLEMS 8

REFERENCES 9

2 VARYING-PROBABILITY SAMPLING 11

2.1 Introduction 11

2.2 Obtaining Varying-Probability Samples 11

2.3 Sampling Designs(Ordered and Unordered) 15

2.4 Sufficiency in Sampling from Finite Populations 19

2.5 Sampling with Varying Probabilities and Without Replacement 23

PROBLEMS 26

REFERENCES 27

3 SIMPLE RANDOM SAMPLING 28

3.1 Introduction 28

3.2 Notation 29

3.3 Properties of Estimates 30

3.4 Variances of Estimators 31

3.5 Confidence Intervals 33

3.6 Alternate Method for Evaluating var(？) 34

3.7 Random Sampling with Replacement 35

3.8 Estimates for Ratios 36

3.9 Estimates of Means or Totals over Subpopulations 38

3.10 Justification of the Normal Approximation 38

3.11 Asymptotic Normality of Estimates Arising from Simple Random Sampling 38

3.12 Best Unbiased Estimators 40

3.13 Distinct Units 42

3.14 The Distribution of W 44

3.15 Comparison of Simple Random Sampling with and without Replacement 49

3.16 Use of Balanced Incomplete Block Designs in Simple Random Sampling 51

3.17 Estimating Proportions and Percentages 52

3.18 Binomial and Hypergeometric Distributions and Their Use in Sampling 54

3.19 Confidence Limits for M 55

3.20 Confidence Intervals for Unknown Discrete Population Parameter 55

3.21 Use of the Finite Population Correction for Binomial Confidence Limits 57

3.22 Cluster Sampling:Estimation of Proportions 57

PROBLEMS 59

REFERENCES 63

4 ESTIMATION OFTHE SAMPLE SIZE 64

4.1 Introduction 64

4.2 Sample Size in Estimating Proportions 64

4.3 Inverse Sampling for Rare Attributes 66

4.4 Estimating Sample Size with Continuous Data 68

4.5 Estimation of S2 68

4.6 Estimation by Double Sampling 69

4.7 Estimation with Given Variance:Single Unknown Parameter 69

4.8 Sampling Procedure 69

4.9 Estimation of P with Specified Variance V 70

4.10 Estimation of P with Specified CV=C1/2 71

4.11 Estimation of ？with Specified CV=C1/2 71

4.12 Estimation of ？ with Specified Variance V 71

4.13 Computing Sample Size:Decision-Theoretic Approach 72

PROBLEMS 73

REFERENCES 74

5 STRATIFIED SAMPLING 75

5.1 Introduction 75

5.2 Estimators of Mean and Total and Their Properties 76

5.3 Confidence Limits(CI's) 78

5.4 Optimum Allocation of a Random Sample 79

5.5 Merits of Stratified Sampling(SS)Relative to Simple Random Sampling(SRS) 82

5.6 Modification of Optimal Allocation 84

5.7 Estimation of Sample Sizes in Stratified Sampling:Continuous Response Data 85

5.8 Estimation of the Population Mean ？ 85

5.9 Estimation of the Population Total 86

5.10 Application to Stratified Sampling for Proportions 86

5.11 Minimum Variance for Fxed n(Total Sample Size) 87

5.12 Gain by Stratified Sampling for Proportions 87

5.13 Sample Size for Proportions 88

5.14 Poststratification 89

5.15 How Should the Strata be Formed?2 92

5.16 Optimal Choice of L and n 100

5.17 Optimal Choice of L and n Via a Regression Variable 101

5.18 Controlled Sampling 103

5.19 Multiple Stratification 104

5.20 Interpenetrating Subsampling 105

PROBLEMS 108

REFERENCES 114

6 RATIO ESTIMATORS 116

6.1 Introduction 116

6.2 Variance of the Ratio Estimate 117

6.3 Estimates for var(？R) 117

6.4 Confidence Intervals for R 118

6.5 Efficiency Comparisons 118

6.6 An Optimum Property of the Ratio Estimators 120

6.7 Bias in the Ratio Estimate 123

6.8 An Exact Expression for the Bias of the Ratio Estimate 124

6.9 Ratio Estimates in Stratified Random Sampling 125

6.10 Comparison of ？Rs and ？Rc 126

6.11 Optimum Allocation with a Ratio Estimator 127

6.12 Unbiased Ratio Estimates 128

6.13 Jackknife Method for Obtaining a Ratio Estimate with Bias O(n-2) 128

6.14 Multivariate Ratio Estimators 130

6.15 A Dual Ratio Estimator 131

6.16 Comparison of Various Estimators 132

6.17 Unbiased Ratio Estimator 134

PROBLEMS 134

REFERENCES 142

7 REGRESSION ESTIMATORS 143

7.1 Introduction 143

7.2 Properties of Regression Estimators 144

7.3 Sample Estimate of Variance 147

7.4 Comparison of Regression,Ratio Estimates,and the Sample Mean 147

7.5 Properties of the Regression Estimator under a Super Population Model 149

7.6 Regression Estimates in Stratiffed Sampling 150

7.7 Sample Estimates 151

7.8 Unbiased Regression Estimation 154

PROBLEMS 156

REFERENCES 161

8 SYSTEMATIC SAMPLING 162

8.1 Circular Systematic Sampling 162

8.2 Relation to Cluster Sampling 163

8.3 Mean of the Systematic Sample 163

8.4 Variance of the Systematic Mean 164

8.5 An Alternate Form for the Variance of ？sy 164

8.6 Estimation of Sampling Variance 166

8.7 Populations in Random Order 169

8.8 Populations having Linear Trend 170

8.9 Further Developments in Systematic Sampling 171

8.10 Other Super Population Models 173

PROBLEMS 174

REFERENCES 176

9 CLUSTER SAMPLING 177

9.1 Necessity of Cluster Sampling 177

9.2 Notation 178

9.3 Precision of Survey Data 179

9.4 Relation between Variance and Intracluster Correlation 180

9.5 Estimation of M 182

9.6 Cost Analysis 182

9.7 Custer Sampling for Proportions 185

9.8 Case of Unequal Cluster Sizes 186

9.9 Probability Sampling Proportional to Size 188

9.10 Comparison of the Three Methods 192

PROBLEMS 193

REFERENCES 194

10 VARYING PROBABILITY SAMPLING:WITHOUT REPLACEMENT 196

10.1 Introduction and Preliminaries 196

10.2 Expected Values of Sums and Product-Sums 199

10.3 Estimation of the Population Total 200

10.4 Application of the Theory 204

10.5 Systematic Sampling:Unequal Probabilities 215

10.6 A New Systematic Sampling with an Unbiased Estimate of the Variance 220

10.7 Computing Inclusion Probabilities and Estimation Procedures 222

PROBLEMS 227

REFERENCES 228

11 TWO-PHASE AND REPETITIVE SAMPLING 229

11.1 Introduction 229

11.2 Difference Estimation 229

11.3 Unbiased Ratio Estimation 232

11.4 Biased Ratio Estimation 232

11.5 Regression Estimation 233

11.6 Estimation by Stratification 237

11.7 Repetitive Surveys 239

PROBLEMS 242

REFERENCES 245

12 TWO-STAGE SAMPLING 246

12.1 Introduction 246

12.2 Notation 247

12.3 Estimation of Population Totals 247

12.4 Two-Stage Scheme with Simple Random Sampling 248

12.5 Comparison with Single-Stage and Custer Sampling 252

12.6 Probability Sampling for a Two-Stage Design 255

PROBLEMS 259

REFERENCES 262

13 NONSAMPLING ERRORS 263

13.1 Introduction 263

13.2 Effect of Nonresponse on Sample Mean and Proportion 264

13.3 Required Sample Size When Nonresponse Is Present 265

13.4 Conditional Inference When Nonresponse Exists 269

13.5 Call-Backs 269

13.6 A Probabilistic Model for Nonresponse 276

13.7 Randomized Responses to Sensitive Questions 280

13.8 Measurement Errors 284

PROBLEMS 286

REFERENCES 288

14 BAYESIAN APPROACH FOR INFERENCE IN FINITE POPULATIONS 289

14.1 Introduction 289

14.2 Notation and the Model 289

14.3 Some Basic Results 291

14.4 Simple Random Sampling 292

14.5 Hypergeometric-Binomial Model 294

14.6 Stratified Sampling 298

14.7 Two-Stage Sampling 300

14.8 Response Error and Bias 304

PROBLEMS 306

REFERENCES 308

15 THE JACKKNIFE METHOD 309

15.1 Introduction 309

15.2 The General Method 309

15.3 Main Applications 316

15.4 Interval Estimation 317

15.5 Transformations 317

15.6 The Bias in the Jackknife Estimate of the Variance 318

PROBLEMS 322

REFERENCES 322

16 THE BOOTSTRAP METHOD 324

16.1 Introduction 324

16.2 The Bootstrap Method 324

16.3 Bootstrap Methods for General Problems 326

16.4 The Bootstrap Estimate of Bias 327

16.5 Case of Finite Sample Space 327

16.6 Regression Problems 329

16.7 Bootstrap Confidence Intervals 332

16.8 Application of Bootstrap Methods in Finance and Management Cases 333

PROBLEMS 333

REFERENCES 334

17 SMALL-AREA ESTIMATION 335

17.1 Introduction 335

17.2 Demographic Methods 336

17.3 Multiple Regression Methods 338

17.4 Synthetic Estimators 340

17.5 Composite Estimators 341

PROBLEMS 344

REFERENCES 345

18 IMPUTATIONS IN SURVEYS 347

18.1 Introduction 347

18.2 General Rules for Imputing 348

18.3 Methods of Imputation 349

18.4 Evaluation of Imputation Procedures 351

18.5 Secondary Data Analysis with Missing Observations 353

18.6 A Procedure for Assessing the Quality of Inferences 354

18.7 Bayesian Method 356

18.8 Comparison of the Various Imputation Methods 361

18.9 Multiple Imputation for Interval Estimation 362

18.10 Normal-Based Analysis of a Multiple Imputed Data Set 363

18.11 Confidence Interval for Population Mean Following Multiple Imputation 366

PROBLEMS 371

REFERENCES 372

Answers to Selected Problems 375

List of Cumulative References 401

Author Index 408

Subject Index 411