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Ranked Set Sampling
Theory and Applications
By: Zehua Chen, Zhidong Bai, Bimal Sinha
Paperback | 28 November 2003
At a Glance
244 Pages
22.86 x 15.24 x 1.27
Paperback
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This is the first book on the concept and applications of ranked set sampling. It provides a comprehensive review of the literature, and it includes many new results and novel applications.
Scientists and researchers on this subject will find a balanced presentation of theory and applications. The mathematical rigor of the theoretical foundations makes it beneficial to researchers. The detailed description of various methods illustrated by real or simulated data makes it useful for scientists and practitioners in application areas such as agriculture, forestry, sociology, ecological and environmental science, and medical studies. It can serve as a reference book and as a textbook for a short course at the graduate level.
Zehua Chen is Associate Professor of Statistics at the National University of Singapore. Zhidong Bai is Professor of Statistics at the National University of Singapore; he is a Fellow of the Institute of Mathematical Statistics. Bimal Sinha is the Presidential Research Professor at University of Maryland Baltimore County; he is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
"This comprehensive and up-to-date monograph covers, systematically and in simple language, the theory and applications of ranked set sampling (RSS), an improved technique related to traditional simple random sampling (SRS). Strong emphasis is placed on theoretical developments in RSS. In the meanwhile, the practical orientation and broad coverage will appeal to researchers and scientists working in sampling techniques, experimental designs, nonparametric statistics, and related fields...I would highly recommend this well-written and reasonably priced book." Techometrics, February 2005
"Ranked Set Sampling: Theory and Applications represents a major achievement, providing an up-to-date account of major research in ranked set sampling....this book would be a good addition to the library of anyone involved in statistical, environmental, and ecological research." Journal of the American Statistical Association, September 2005
"The book is well laid out with concepts well explained...Those who are recently getting interested in the topic will find it an excellent start." Biometrics, December 2005
Industry Reviews
From the reviews:
"This comprehensive and up-to-date monograph covers, systematically and in simple language, the theory and applications of ranked set sampling (RSS), an improved technique related to traditional simple random sampling (SRS). Strong emphasis is placed on theoretical developments in RSS. In the meanwhile, the practical orientation and broad coverage will appeal to researchers and scientists working in sampling techniques, experimental designs, nonparametric statistics, and related fields...I would highly recommend this well-written and reasonably priced book." Techometrics, February 2005
"Ranked Set Sampling: Theory and Applications represents a major achievement, providing an up-to-date account of major research in ranked set sampling....this book would be a good addition to the library of anyone involved in statistical, environmental, and ecological research." Journal of the American Statistical Association, September 2005
"The book is well laid out with concepts well explained...Those who are recently getting interested in the topic will find it an excellent start." Biometrics, December 2005
"This is the first monograph on ranked set sampling (RSS). ... The book presents a happy mixture of theory and applications. Indeed, theoretical foundations are provided with mathematical rigor, and various methods are illustrated by real or simulated data. ... The book will be used as a common reference by statisticians as well as practitioners in agriculture, sociology, ecological and medical studies, etc. It can serve as a textbook for a short course at the graduate level." (Oleksandr Kukush, Zentralblatt MATH, Vol. 1045 (20), 2004)
"This comprehensive and up-to-date monograph covers, systematically and in simple language, the theory and applications of ranked set sampling (RSS) ... . the practical orientation and broad coverage will appeal to researchers and scientists workingin sampling techniques, experimental designs, nonparametric statistics, and related fields. ... I would highly recommend this well-written and reasonably priced book to researchers and practitioners, all of whom are likely to use one or more of the methods it discusses." (Chunming Zhang, Technometrics, Vol. 47 (1), February, 2005)
"This is the first book on the concept and applications of ranked set sampling. It provides a comprehensive review of the literature, and it includes many new results and novel applications. The mathematical rigor of the theoretical foundations makes it beneficial to researchers. The detailed description of various methods illustrated by real or simulated data makes it useful for scientists and practitioners ... . It can serve as a reference book and as a textbook for a short course at the graduate level." (L'Enseignement Mathematique, Vol. 50 (1-2), 2004)
| Introduction | p. 1 |
| What is ranked set sampling? | p. 1 |
| A historical note | p. 7 |
| Scope of the rest of the monograph | p. 8 |
| Balanced Ranked Set Sampling I: Nonparametric | p. 11 |
| Ranking mechanisms | p. 12 |
| Estimation of means using ranked set sample | p. 14 |
| Estimation of smooth-function-of-means using ranked set sample | p. 18 |
| Estimation of variance using an RSS sample | p. 20 |
| Naive moment estimates | p. 20 |
| Minimum variance unbiased non-negative estimate | p. 22 |
| Tests and confidence intervals for population mean | p. 24 |
| Asymptotic pivotal method | p. 25 |
| Choice of consistent estimates of [Sigma]X[subscript RSS] | p. 25 |
| Comparison of power between tests based on RSS and SRS | p. 29 |
| Estimation of quantiles | p. 29 |
| Ranked set sample quantiles and their properties | p. 29 |
| Inference procedures for population quantiles based on ranked set sample | p. 32 |
| The relative efficiency of RSS quantile estimate with respect to SRS quantile estimate | p. 35 |
| Estimation of density function with ranked set sample | p. 35 |
| RSS density estimate and its properties | p. 36 |
| The relative efficiency of the RSS density estimate with respect to its SRS counterpart | p. 40 |
| M-estimates with RSS data | p. 44 |
| The RSS M-estimates and their asymptotic properties | p. 44 |
| The relative efficiency of the RSS M-estimates | p. 46 |
| Appendix: Technical details for Section 2.4 | p. 46 |
| Bibliographic notes | p. 50 |
| Balanced Ranked Set Sampling II: Parametric | p. 53 |
| The Fisher information of ranked set samples | p. 54 |
| The Fisher information of ranked set samples when ranking is perfect | p. 54 |
| The Fisher information of ranked set samples when ranking is imperfect | p. 58 |
| The maximum likelihood estimate and its asymptotic relative efficiency | p. 63 |
| The best linear unbiased estimation for location-scale families | p. 66 |
| The regularity conditions and the existence of Fisher information matrix of ranked set samples | p. 68 |
| Bibliographic notes | p. 71 |
| Unbalanced Ranked Set Sampling and Optimal Designs | p. 73 |
| General structure of unbalanced RSS | p. 74 |
| Nonparametric analysis of unbalanced ranked-set data | p. 75 |
| Asymptotic properties of unbalanced ranked-set sample quantiles | p. 75 |
| Nonparametric estimation of quantiles and distribution function | p. 76 |
| Confidence interval and hypothesis testing | p. 78 |
| Estimation of statistical functionals | p. 79 |
| Inference by bootstrapping | p. 82 |
| Simulation results | p. 82 |
| Parametric analysis of unbalanced ranked-set data | p. 84 |
| Optimal design for location-scale families | p. 86 |
| Optimal RSS for MLE | p. 86 |
| Optimal RSS for BLUE | p. 91 |
| Optimal design for estimation of quantiles | p. 91 |
| Optimal RSS scheme for the estimation of a single quantile | p. 91 |
| Optimal RSS scheme for the simultaneous estimation of several quantiles | p. 94 |
| The computation of optimal designs | p. 95 |
| Asymptotic relative efficiency of the optimal schemes | p. 96 |
| Asymptotic relative efficiency of the optimal schemes for parametric location-scale families | p. 96 |
| Relative efficiency of the optimal schemes for the estimation of quantiles | p. 97 |
| Other design methodologies | p. 98 |
| Bayesian design | p. 99 |
| Adaptive design | p. 99 |
| Bibliographic notes | p. 100 |
| Distribution-Free Tests with Ranked Set Sampling | p. 103 |
| Sign test with RSS | p. 103 |
| Distributional properties of S[superscript + subscript RSS] | p. 104 |
| Decision rules of the sign test and confidence intervals for median | p. 110 |
| Effect of imperfect ranking on RSS sign test | p. 110 |
| Comparison of efficiency and power with respect to S[superscript + subscript SRS] | p. 113 |
| Mann-Whitney-Wilcoxon test with RSS | p. 115 |
| Distributional properties of U[subscript RSS] | p. 117 |
| Decision rules of the RSS Mann-Whitney-Wilcoxon test | p. 122 |
| The estimate and confidence interval of [Delta] | p. 123 |
| Effect of imperfect ranking on RSS Mann-Whitney-Wilcoxon test | p. 124 |
| Wilcoxon signed rank test with RSS | p. 124 |
| Distributional properties of W[superscript + subscript RSS] | p. 125 |
| Decision rules of the Wilcoxon signed rank test | p. 130 |
| Estimation of [theta] | p. 131 |
| Effect of imperfect ranking on RSS Wilcoxon signed rank test | p. 133 |
| Optimal design for distribution-free tests | p. 133 |
| Optimal design for sign test | p. 133 |
| Optimal design for Wilcoxon signed rank tests | p. 135 |
| Bibliographic notes | p. 142 |
| Ranked Set Sampling with Concomitant Variables | p. 143 |
| Multi-layer ranked set sampling | p. 144 |
| Motivation and definition | p. 144 |
| Consistency of multi-layer ranked set sampling | p. 146 |
| Comparison between multi-layer RSS and marginal RSS by simulation studies | p. 147 |
| Issues on the choice of concomitant variables | p. 150 |
| Adaptive ranked set sampling | p. 151 |
| The best ranking mechanism | p. 151 |
| Adaptive ranked set sampling procedure | p. 152 |
| A simulation study | p. 153 |
| Regression analysis based on RSS with concomitant variables | p. 155 |
| Estimation of regression coefficients with RSS | p. 156 |
| Regression estimate of the mean of Y with RSS | p. 157 |
| Comparison of the RSS regression estimate and the ordinary RSS estimate | p. 158 |
| How does a specific ranking mechanism affect the efficiency of the regression estimate? | p. 160 |
| Optimal RSS schemes for regression analysis | p. 161 |
| Asymptotically optimal criteria | p. 162 |
| Asymptotically optimal schemes for simple linear regression | p. 164 |
| Applications | p. 166 |
| Technical details | p. 170 |
| Bibliographic notes | p. 174 |
| Ranked Set Sampling as Data Reduction Tools | p. 175 |
| Remedian: a motivation | p. 175 |
| Repeated ranked-set procedure for a single quantile | p. 177 |
| Repeated ranked-set procedure for multiple quantiles | p. 180 |
| Balanced repeated ranked-set procedure | p. 184 |
| Procedure for multivariate populations | p. 186 |
| Case Studies | p. 191 |
| Plantations of cinchona | p. 191 |
| Cost effective gasoline sampling | p. 194 |
| Estimation of weights of browse and herbage | p. 195 |
| Estimation of shrub phytomass in Appalachian oak forests | p. 198 |
| Single family homes sales price data | p. 201 |
| Tree data | p. 202 |
| References | p. 213 |
| Index | p. 223 |
| Table of Contents provided by Rittenhouse. All Rights Reserved. |
ISBN: 9780387402635
ISBN-10: 0387402632
Series: LECTURE NOTES IN STATISTICS
Published: 28th November 2003
Format: Paperback
Language: English
Number of Pages: 244
Audience: General Adult
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 22.86 x 15.24 x 1.27
Weight (kg): 0.35
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