Ranked set sampling (RSS) gives a new approach to dealing with sample selection. It was proposed
in the seminal paper of McIntyre (1952. A method for unbiased selective sampling using ranked
sets. Australian Journal of Agricultural Research 3, 385À390). His experience in agricultural appli-
cation provoked a challenge to the usual simple random sampling (SRS) design introducing a previ-
ous ordering of the units. The practical studies suggested that it produces more accurate estimators
of the mean. This proposal was taken into account by other practitioners dealing with agricultural
studies. They also obtained better results using RSS. The mathematical validity of the claim was
sustained by the work of Takahasi and Wakimoto (1968. On unbiased estimates of the population
mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical
Mathematics 20, 1À31).
That fact also remained unnoticed by the majority of the statistical community but some inter-
esting results were developed for establishing the mathematical reasons sustaining having better
results when using RSS.
Author(s): Carlos N. Bouza-Herrera, Amer Ibrahim Falah Al-Omari
Publisher: Academic Press
Year: 2019
Language: English
Pages: 295
Cover......Page 1
Ranked Set Sampling: 65 Years Improving the Accuracy
in Data Gathering
......Page 3
Copyright......Page 4
List of Contributors......Page 5
Preface......Page 7
1.1 Introduction......Page 10
1.2 Ranking Ordered Categorical Variables......Page 11
1.3 A Randomized Response Strategy......Page 13
1.4 Evaluation of the Performance of pˆcW......Page 14
References......Page 16
2.1 Introduction......Page 18
2.2 Shewhart Control Chart Under Repetitive Sampling......Page 22
2.3 Ranked Set Sampling Scheme......Page 23
2.3.1 Shewhart Control Charts Under the RSS Scheme......Page 25
2.4 Shewhart Control Chart Under Ranked Repetitive Sampling......Page 26
2.5 Performances of the Proposed Control Chart......Page 27
2.5.1 Comparative Study: Monte Carlo Experiment 2......Page 29
2.6 Concluding Remarks......Page 31
References......Page 32
3.1 Introduction......Page 34
3.2.1 Ranked Set Sampling......Page 35
3.2.2 Extreme Ranked Set Sampling......Page 36
3.3.1 The First Suggested Estimator......Page 37
3.3.2 The Second Suggested Estimator......Page 39
3.3.3 The Third Suggested Estimator......Page 40
3.4 Simulation Study......Page 41
References......Page 51
4.1 Introduction......Page 52
4.1.1 Estimation of Distribution Function Using Method of Moments......Page 55
4.1.2 Estimation of Distribution Function Using Maximum Likelihood Estimator......Page 57
4.2 MERSS Based on Minima......Page 60
4.3 Estimation of F(x) Using Moving Extreme RSS Based on Minima and Maxima......Page 62
4.3.1 MERSS Based on Both Minima and Maxima......Page 63
References......Page 65
Further Reading......Page 67
5.1 Introduction......Page 68
5.2 Statistical Inference for RSS......Page 69
5.3 Bootstrap Method......Page 71
5.4 Numerical Study......Page 72
5.5 Conclusions......Page 76
Further Reading......Page 79
6.1 Introduction......Page 80
6.2 The Considered Scrambling Procedures......Page 81
6.3 Using Order Statistics (OS) for Scrambling......Page 83
References......Page 86
Further Reading......Page 87
7.1 Introduction......Page 88
7.2 Ratio Type Estimators in SRSWR Using γ......Page 90
7.3.1 Some Basic Elements of RSS......Page 92
7.3.2 Ratio Type Estimators......Page 94
7.4 A Numerical Study of the Effect of a Vaccine for Lung Cancer......Page 97
References......Page 100
Further Reading......Page 102
8.1 Introduction......Page 103
8.2.1 Ranked Set Sampling......Page 105
8.2.2 Paired Ranked Set Sampling......Page 106
8.2.4 Double-Ranked Set Sampling......Page 107
8.2.5 Partially Ordered Judgment Subset Sampling......Page 108
8.3.1 Paired Partially Ordered Judgment Subset Sampling......Page 109
8.3.2 L Partially Ordered Judgment Subset Sampling......Page 111
8.3.3 Ranked Partially Ordered Judgment Subset Sampling......Page 113
8.4 Efficiency Comparisons......Page 117
8.6 Conclusions......Page 119
References......Page 123
9.1 Introduction......Page 125
9.2.3 Ranked Set Sampling With Unequal Samples for Skew Distributions......Page 126
9.3 Estimation of the Population Mean......Page 127
9.4 Comparisons of Estimators......Page 129
9.5 More Ranked Set Sampling Procedures with Unequal Samples......Page 130
9.6 Applications to Real-World Data......Page 131
References......Page 132
10.1 Introduction......Page 134
10.2.1 Ranked Set Sample Mean as an Estimator of θ2......Page 137
10.2.3 Estimation of θ2 Based on Unbalanced Multistage Ranked Set Sampling......Page 138
10.2.4 Estimation of θ2 Based on Unbalanced Single-Stage Ranked Set Sampling......Page 140
10.2.5 Estimation of θ2 Based on Unbalanced Steady-State Ranked Set Sampling......Page 141
10.3.1 Relative Efficiency......Page 143
10.4 Conclusion......Page 145
References......Page 146
11.1 Introduction......Page 149
11.2 Review of RSS in FGM Family of Distribution......Page 150
11.3 The Suggested Family of Estimators for the Scale Parameter θ2 Based on the a priori Interval......Page 153
11.4 Relative Efficiency......Page 155
References......Page 160
12.1 Introduction......Page 162
12.2 Stratified Ranked Set Sample......Page 164
12.3 Statistical Inference......Page 165
12.4 Estimators of Variance and MSPE......Page 167
12.5 Empirical Results......Page 168
12.6 Example......Page 169
12.7 Concluding Remarks......Page 171
References......Page 173
Appendix......Page 174
13.1 Introduction......Page 176
13.2 Ahmed, Sedory, and Singh Model......Page 177
13.3 Proposed Ranked Set Sampling Randomized Response Model......Page 179
13.4 Efficiency of Ranked Set Sampling......Page 185
References......Page 188
Appendix A......Page 189
14.1 Introduction......Page 194
14.2 Proposed Forced Quantitative Randomized Response Model......Page 197
14.4 Relative Efficiency......Page 200
References......Page 202
Appendix A......Page 204
15.2 Stratified Random Sampling......Page 207
15.3 Stratified Ranked Set Sampling......Page 210
15.4 Numerical Illutrations......Page 213
References......Page 220
16.1 Introduction......Page 222
16.2 Notations and Basic Results......Page 223
16.3 Two-Stage Ranked Set Sampling......Page 227
16.4 Calibrated Estimator in Two-Stage Ranked Set Sampling......Page 229
16.5 Numerical Illustration With Real Data......Page 232
References......Page 235
Appendix A......Page 237
17.2 Estimation of Population Mean Using Single Auxiliary Attribute Information......Page 241
17.3 Estimation of Population Mean Using Two (or More) Auxiliary Attribute Information......Page 246
References......Page 249
18.1 Introduction......Page 252
18.2 Some Existing Estimators for the Population Mean......Page 254
18.3.1 Generalized Exponential Estimators Using RSS......Page 255
18.4 A Simulation Study......Page 256
References......Page 258
19.1 Introduction......Page 259
19.2 Extropy Estimation Using a Ranked Set Sample......Page 260
19.3 Extropy-Based Tests of Uniformity in RSS......Page 262
References......Page 266
Further Reading......Page 267
20.1 Introduction......Page 268
20.3.1 Balanced Ranked Set Sampling......Page 269
20.3.2 Unbalanced Ranked Set Sampling......Page 270
Function Code......Page 271
Function Code......Page 272
Arguments......Page 273
20.4 Estimation Using RSS......Page 274
20.5.1 Ranking with an inexpensive quantitative measurement......Page 275
20.5.2 Ranking with a professional judgment......Page 276
Acknowledgments......Page 277
Further Reading......Page 278
21.1 Introduction......Page 279
21.2 Estimation of the Treatment Effects in a One-Way Layout in Ranked Set Sampling......Page 280
21.3 Estimation of the Variance in RSS......Page 281
21.4.1 Normality-Based Tests......Page 283
21.4.2 Analysis of the Time to Death of HIV-Infected Persons......Page 287
References......Page 288
Index......Page 289
Back Cover......Page 295
