{"product_id":"pitman-s-measure-of-closeness-a-comparison-of-statistical-estimatiors-a-comparison-of-statistical-estimators-paperback-softback-9780898713084","title":"Pitman`s Measure of Closeness – A Comparison of Statistical Estimatiors; A Comparison of Statistical Estimators (Paperback \/ softback) 9780898713084","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003ePitman`s Measure of Closeness – A Comparison of Statistical Estimatiors\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eA Comparison of Statistical Estimators\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThis book provides a thorough introduction to the methods and known results associated with PMC.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJerome P. Keating (Author), Robert L. Mason (Author), Pranab K. Sen (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780898713084\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 31 January 1994\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e240 pages\u003cbr\u003e25.1 x 17.7 x 1.4 cm, 0.438 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e' … a comprehensive survey of recent contributions to the subject. It discusses the merits and deficiencies of PMC, throws light on recent controversies, and formulates new problems for further research. Finally, there is a need for such a book, as PMC is not generally discussed in statistical texts. Its role in estimation theory and its usefulness to the decision maker are not well known. . . The contributions by the authors of this book have been especially illuminating in resolving some of the controversies surrounding PMC.' C. R. Rao, from the foreword\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003ePitman's Measure of Closeness (PMC) is simply an idea whose time has come. Certainly there are many different ways to estimate unknown parameters, but which method should you use? Posed as an alternative to the concept of mean-squared-error, PMC is based on the probabilities of the closeness of competing estimators to an unknown parameter. Renewed interest in PMC over the last 20 years has motivated the authors to produce this book, which explores this method of comparison and its usefulness. Written with research oriented statisticians and mathematicians in mind, but also considering the needs of graduate students in statistics courses, this book provides a thorough introduction to the methods and known results associated with PMC. Following a foreword by C .R. Rao, the first three chapters focus on basic concepts, history, controversy, paradoxes and examples associated with the PMC criterion.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Part I. Introduction\u003cbr\u003e 1. Evolution of Estimation Theory\u003cbr\u003e Least Squares\u003cbr\u003e Method of Moments\u003cbr\u003e Maximum Likelihood\u003cbr\u003e Uniformly Minimum Variance Unbiased Estimation\u003cbr\u003e Biased Estimation\u003cbr\u003e Bayes and Empirical Bayes\u003cbr\u003e Influence Functions and Resampling Techniques\u003cbr\u003e Future Directions\u003cbr\u003e 2. PMC Comes of Age\u003cbr\u003e PMC: A Product of Controversy\u003cbr\u003e PMC as an Intuitive Criterion\u003cbr\u003e 3. The Scope of the Book\u003cbr\u003e History, Motivation, and Controversy of PMC\u003cbr\u003e A Unified Development of PMC\u003cbr\u003e Part II. Development of Pitman's Measure of Closeness: 1. The Intrinsic Appeal of PMC\u003cbr\u003e Use of MSE\u003cbr\u003e Historical Development of PMC\u003cbr\u003e Convenience Store Example\u003cbr\u003e 2. The Concept of Risk\u003cbr\u003e Renyi's Decomposition of Risk\u003cbr\u003e How Do We Understand Risk?\u003cbr\u003e 3. Weakness in the Use of Risk\u003cbr\u003e When MSE Does Not Exist\u003cbr\u003e Sensitivity to the Choice of the Loss Function\u003cbr\u003e The Golden Standard\u003cbr\u003e 4. Joint Versus Marginal Information\u003cbr\u003e Comparing Estimators with an Absolute Ideal\u003cbr\u003e Comparing Estimators with One Another\u003cbr\u003e 5. Concordance of PMC with MSE and MAD\u003cbr\u003e Part III. Anomalies with PMC: 1. Living in an Intransitive World\u003cbr\u003e Round-Robin Competition\u003cbr\u003e Voting Preferences\u003cbr\u003e Transitiveness\u003cbr\u003e 2. Paradoxes Among Choice\u003cbr\u003e The Pairwise-Worst Simultaneous-Best Paradox\u003cbr\u003e The Pairwise-Best Simultaneous-Worst Paradox\u003cbr\u003e Politics: The Choice of Extremes\u003cbr\u003e 3. Rao's Phenomenom\u003cbr\u003e 4. The Question of Ties\u003cbr\u003e Equal Probability of Ties\u003cbr\u003e Correcting the Pitman Criterion\u003cbr\u003e A Randomized Estimator\u003cbr\u003e 5. The Rao-Berkson Controversy\u003cbr\u003e Minimum Chi-Square and Maximum Likelihood\u003cbr\u003e Model Inconsistency\u003cbr\u003e Remarks\u003cbr\u003e Part 4. Pairwise Comparisons\u003cbr\u003e 1. Geary-Rao Theorem\u003cbr\u003e 2. Applications of the Geary-Rao Theorem\u003cbr\u003e 3. Karlin's Corollary\u003cbr\u003e 4. A Special Case of the Geary-Rao Theorem\u003cbr\u003e Surjective Estimators\u003cbr\u003e The MLR Property\u003cbr\u003e 5. Applications of the Special Case\u003cbr\u003e 6. Transitiveness\u003cbr\u003e Transitiveness Theorem\u003cbr\u003e Another Extension of Karlin's Corollary\u003cbr\u003e Part V. Pitman-Closest Estimators: 1. Estimation of Location Parameters\u003cbr\u003e 2. Estimators of Scale\u003cbr\u003e 3. Generalization via Topological Groups\u003cbr\u003e 4. Posterior Pitman Closeness\u003cbr\u003e 5. Linear Combinations\u003cbr\u003e 6. Estimation by Order Statistics\u003cbr\u003e Part 6. Asymptotics and PMC\u003cbr\u003e 1. Pitman Closeness of BAN Estimators\u003cbr\u003e Modes of Convergence\u003cbr\u003e Fisher Information\u003cbr\u003e BAN Estimates are Pitman Closet\u003cbr\u003e 2. PMC by Asymptotic Representations\u003cbr\u003e A General Proposition\u003cbr\u003e 3. Robust Estimation of a Location Parameter\u003cbr\u003e L-Estimators\u003cbr\u003e M-Estimators\u003cbr\u003e R-Estimators\u003cbr\u003e 4. APC Characterizations of Other Estimators\u003cbr\u003e Pitman Estimators\u003cbr\u003e Examples of Pitman Estimators\u003cbr\u003e PMC Equivalence\u003cbr\u003e Bayes Estimators\u003cbr\u003e 5. Second-Order Efficiency and PMC\u003cbr\u003e Asymptotic Efficiencies\u003cbr\u003e Asymptotic Median Unbiasedness\u003cbr\u003e Higher-Order PMC\u003cbr\u003e Index\u003cbr\u003e Bibliography.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Miscellaneous items [\u003ca title=\"See our other books on Miscellaneous items\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Miscellaneous%20items%20%5BWZ%5D%22\"\u003eWZ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"MP–SIA SIAM – Society for Industrial and Applied M","offers":[{"title":"Brand New","offer_id":52410746110232,"sku":"9780898713084","price":45.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780898713084i.jpg?v=1784251360","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/pitman-s-measure-of-closeness-a-comparison-of-statistical-estimatiors-a-comparison-of-statistical-estimators-paperback-softback-9780898713084","provider":"Freshly Printed Books","version":"1.0","type":"link"}