Ranked Set Sampling : 65 Years Improving the Accuracy in Data Gathering

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. Cover......Page 1 Ranked Set Sampling: 65 Years Improving the Accuracyin 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 Ranked Set Sampling: 65 Years Improving the Accuracy in Data Gathering is an advanced survey technique which seeks to improve the likelihood that collected sample data presents a good representation of the population and minimizes the costs associated with obtaining them. The main focus of many agricultural, ecological and environmental studies is the development of well designed, cost-effective and efficient sampling designs, giving RSS techniques a particular place in resolving the disciplinary problems of economists in application contexts, particularly experimental economics. This book seeks to place RSS at the heart of economic study designs. Focuses on how researchers should manipulate RSS techniques for specific applications Discusses RSS performs in popular statistical models, such as regression and hypothesis testing Includes a discussion of open theoretical research problems Provides mathematical proofs, enabling researchers to develop new models "Ranked Set Sampling: 65 Years Improving the Accuracy in Data Gathering is an advanced survey technique which seeks to improve the likelihood that collected sample data presents a good representation of the population and minimizes the costs associated with obtaining them. The main focus of many agricultural, ecological and environmental studies is the development of well designed, cost-effective and efficient sampling designs, giving RSS techniques a particular place in resolving the disciplinary problems of economists in application contexts, particularly experimental economics. This book seeks to place RSS at the heart of economic study designs."--Back cover