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Taylor & Francis Ltd Mathematical Statistics Basic Ideas And Selected Topics Vol 1 2Ed 2015 Edition by Peter J. Bickel, Kjell A. Doksum
Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition presents fundamental, classical statistical concepts at the doctorate level. It covers estimation, prediction, testing, confidence sets, Bayesian analysis, and the general approach of decision theory. This edition gives careful proofs of major results and explains how the theory sheds light on the properties of practical methods. The book first discusses non- and semiparametric models before covering parameters and parametric models. It then offers a detailed treatment of maximum likelihood estimates (MLEs) and examines the theory of testing and confidence regions, including optimality theory for estimation and elementary robustness considerations. It next presents basic asymptotic approximations with one-dimensional parameter models as examples. The book also describes inference in multivariate (multiparameter) models, exploring asymptotic normality and optimality of MLEs, Wald and Rao statistics, generalized linear models, and more.Mathematical Statistics: Basic Ideas and Selected Topics, Volume II will be published in 2015. It will present important statistical concepts, methods, and tools not covered in Volume I. STATISTICAL MODELS, GOALS, AND PERFORMANCE CRITERIA Data, Models, Parameters, and StatisticsBayesian Models The Decision Theoretic FrameworkPrediction Sufficiency Exponential FamiliesMETHODS OF ESTIMATION Basic Heuristics of Estimation Minimum Contrast Estimates and Estimating Equations Maximum Likelihood in Multiparameter Exponential FamiliesAlgorithmic IssuesMEASURES OF PERFORMANCE Introduction Bayes Procedures Minimax Procedures Unbiased Estimation and Risk Inequalities Nondecision Theoretic Criteria TESTING AND CONFIDENCE REGIONS Introduction Choosing a Test Statistic: The Neyman-Pearson Lemma Uniformly Most Powerful Tests and Monotone Likelihood Ratio Models Confidence Bounds, Intervals, and RegionsThe Duality between Confidence Regions and Tests Uniformly Most Accurate Confidence Bounds Frequentist and Bayesian Formulations Prediction Intervals Likelihood Ratio ProceduresASYMPTOTIC APPROXIMATIONS Introduction: The Meaning and Uses of Asymptotics Consistency First- and Higher-Order Asymptotics: The Delta Method with Applications Asymptotic Theory in One Dimension Asymptotic Behavior and Optimality of the Posterior DistributionINFERENCE IN THE MULTIPARAMETER CASE Inference for Gaussian Linear Models Asymptotic Estimation Theory in p Dimensions Large Sample Tests and Confidence Regions Large Sample Methods for Discrete Data Generalized Linear Models Robustness Properties and Semiparametric ModelsAPPENDIX A: A REVIEW OF BASIC PROBABILITY THEORYAPPENDIX B: ADDITIONAL TOPICS IN PROBABILITY AND ANALYSISAPPENDIX C: TABLESINDEXProblems and Complements, Notes, and References appear at the end of each chapter.