Advanced Sampling Methods

Foreword......Page 5
Preface......Page 6
Contents......Page 10
1.1 Introduction......Page 17
1.2 Sample Survey......Page 18
1.3 Questionnaire Construction......Page 19
1.4 Population, Sample, and Estimator......Page 20
1.5 Advanced Sampling Methods......Page 22
References......Page 24
2.1.1 Some Population Parameters......Page 26
2.1.2 Some Sample Values or Statistics......Page 27
2.2 Simple Random Sampling with Replacement......Page 28
2.3 Simple Random Sampling Without Replacement......Page 31
2.4 Estimation of Population Proportions......Page 37
2.5 Determination of Sample Size......Page 39
2.6 Use of Auxiliary Information......Page 40
2.6.1 Ratio Method of Estimation......Page 41
2.6.2 Regression Method of Estimation......Page 46
2.7 Exercises......Page 49
3.1 Introduction......Page 51
3.2 Stratified Random Sampling with Proportional Allocation......Page 54
3.3 Stratified Random Sampling with Optimal Allocation......Page 57
3.4 Post-Stratified Random Sampling......Page 61
3.5 Stratified Random Sampling for Proportions......Page 63
3.6 Exercises......Page 65
Reference......Page 67
4.1 Introduction......Page 68
4.2 Comparison of Systematic Sampling with Simple Random Sampling......Page 71
4.3 Comparison of Systematic Sampling with Stratified Random Sampling......Page 72
4.5 Exercises......Page 73
5.1 Introduction......Page 74
5.2.1 Equal Cluster Sizes......Page 75
5.3 Multistage Cluster Sampling......Page 79
5.3.1 Two-stage Cluster Sampling......Page 81
5.4 Exercises......Page 85
References......Page 88
6.2 Ratio Estimator in Double Sampling......Page 89
6.3 Regression Estimator in Double Sampling......Page 92
6.4 Exercises......Page 95
7.2 Probability Proportional to Size Sampling with Replacement......Page 97
7.3 Probability Proportional to Size Sampling Without Replacement......Page 101
7.4.1 Sampford's (ch7Sam67) IPPS Scheme......Page 106
7.4.3 Rao–Hartley–Cochran (RHC) Sampling Strategy......Page 107
7.5 Classes of Linear Estimators......Page 108
References......Page 109
8.1 Introduction......Page 111
8.2 Warner's Randomized Response Design......Page 113
8.3.1 Unrelated Question Design  (ch8Greetal69,ch8Greetal71)......Page 115
8.3.2 Forced Response Design (Boruch ch8Bor71)......Page 117
8.3.3 Disguised Response Design (ch8Kuk90)......Page 118
8.4 Some Case Studies......Page 119
8.5 Exercises......Page 120
References......Page 121
9.1 Introduction......Page 124
9.2.1 Evaluating an Integral......Page 125
9.3 Bootstrapping Method......Page 127
9.4 Jackknife Method......Page 128
9.5 Importance Sampling......Page 130
9.6 Examples......Page 132
References......Page 135
10.1 Introduction......Page 136
10.2 Notations and Terminology......Page 138
10.3 Illustration of Methodology......Page 139
10.4 Sampling Units and their Inclusion Probabilities......Page 142
10.5 Illustration of Computing Inclusion Probabilities......Page 143
10.6 Different Approaches of Estimation......Page 144
10.6.2 Design-Based Approach......Page 145
10.7 Variable Probability Estimation......Page 146
10.8 Estimation of Population Mean/Total without Using the Edge Units......Page 147
10.8.1 Different Estimators in ACS......Page 148
10.8.2 Improved Unbiased Estimators in ACS......Page 151
10.9 Estimation of Population Mean in ACS by using Edge Units......Page 154
10.10.1 Estimation of an Upper Bound for the Population Total......Page 157
10.10.2 Estimation of a Lower Bound for the Population Total......Page 159
10.10.3 Illustrative example of RAS......Page 160
10.11 Estimation of the Final Sample Size in ACS......Page 161
10.12 Pilot Study for Estimating the Final Sample Size......Page 164
10.13 Exercises......Page 165
References......Page 166
11.1 Introduction......Page 168
11.2.2 Selection Procedure......Page 169
11.3.1 Modified HT Estimator......Page 170
11.3.2 Modified HH Estimator......Page 172
11.4 Non-overlapping Clusters Scheme......Page 174
11.5 Illustrative Example......Page 175
11.6 Exercises......Page 179
References......Page 180
12.1 Introduction......Page 181
12.2 Notations and Sampling Design......Page 182
12.3.1  Regression Type Estimator......Page 183
12.4 Exercises......Page 186
References......Page 187
13.1 Introduction......Page 188
13.2.1 Sampling Until k Units of PM are Observed......Page 189
13.2.2 Mixed Design Stopping Rule......Page 190
13.3 Inverse Sampling with Unequal Selection Probabilities......Page 191
13.4 General Inverse Sampling......Page 194
13.5.1 General Inverse Sampling......Page 195
13.6 Inverse Adaptive Cluster Sampling......Page 197
13.7 General Unequal Probability Inverse ACS......Page 198
13.8 Exercises......Page 199
References......Page 201
14.1 Introduction......Page 202
14.2.1 New Design......Page 203
14.2.2 Estimators of Population Total......Page 204
14.3 Simulation Study and Discussion......Page 208
References......Page 211
15.2 Stratified Inverse ACS Design......Page 212
15.3 Simulation Study......Page 215
References......Page 217
16.1 Introduction......Page 218
16.2 Negative Adaptive Cluster Sampling......Page 219
16.2.1 Procedure of NACS......Page 220
16.2.2 Difference in ACS, ACDS, and NACS......Page 221
16.3.1  Modified Ratio Type Estimator......Page 222
16.3.2 Modified Regression Estimator......Page 224
16.3.3 Product Estimator......Page 225
16.4 Sample Survey......Page 226
16.5 Exercises......Page 235
References......Page 236
17.1 Introduction......Page 237
17.2.1 Sampling Design and Notations......Page 238
17.3.1 Regression Estimator......Page 240
17.3.2 Ratio Estimator......Page 241
17.4 Sample Survey......Page 242
17.5 Exercises......Page 247
References......Page 248
18.1 Introduction......Page 249
18.2 Two-Stage NACS......Page 250
18.3.1 Composite HT Estimator......Page 251
18.3.2 Two-Stage Regression Estimator......Page 254
18.4 Sample Survey......Page 257
References......Page 263
19.1 Introduction......Page 264
19.2 Balanced RSS......Page 267
19.3.1 Skewed Underlying Distributions......Page 269
19.3.2 Symmetric Underlying Distributions......Page 273
19.4 Some Important Applications......Page 277
19.6 Exercises......Page 278
References......Page 280
20.2 Estimation of Location and Scale Parameters......Page 282
20.3 Estimating Population Proportion......Page 286
20.4 Quantile Estimation......Page 287
20.5 RSS in Non-parametric Inference......Page 288
20.5.1 One Sample Case......Page 289
20.5.2 Two Sample Case......Page 291
20.6 Exercises......Page 292
References......Page 293
21.2 Extreme RSS (ERSS)......Page 295
21.3 Median Ranked Set Sampling (MRSS)......Page 297
21.4 Double-Ranked Set Sampling (DRSS)......Page 298
21.5.4 Balanced Groups RSS (ch21Jemetal08)......Page 299
21.5.9 Mixed RSS (ch21Haqetal14)......Page 300
21.6 Exercises......Page 301
References......Page 302
22.2 Types of Non-sampling Errors......Page 303
22.2.3 Inadequate Sample Size......Page 304
22.2.5 Non-response Error......Page 305
Reference......Page 307