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| (Note:Each chapter concludes with Problems and Complements, Notes, and References.) | |
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| Statistical Models, Goals, and Performance Criteria | |
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| Data, Models, Parameters, and Statistics | |
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| Bayesian Models | |
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| The Decision Theoretic Framework | |
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| Prediction | |
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| Sufficiency | |
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| Exponential Families | |
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| Methods of Estimation | |
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| Basic Heuristics of Estimation | |
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| Minimum Contrast Estimates and Estimating Equations | |
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| Maximum Likelihood in Multiparameter Exponential Families | |
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| Algorithmic Issues | |
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| Measures of Performance | |
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| Introduction | |
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| Bayes Procedures | |
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| Minimax Procedures | |
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| Unbiased Estimation and Risk Inequalities | |
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| Nondecision Theoretic Criteria | |
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| Testing and Confidence Regions | |
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| Introduction | |
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| Choosing a Test Statistic: The Neyman-Pearson Lemma | |
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| Uniformly Most Powerful Tests and Monotone Likelihood Ratio Models | |
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| Confidence Bounds, Intervals and Regions | |
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| The Duality between Confidence Regions and Tests | |
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| Uniformly Most Accurate Confidence Bounds | |
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| Frequentist and Bayesian Formulations | |
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| Prediction Intervals | |
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| Likelihood Ratio Procedures | |
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| Asymptotic Approximations | |
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| Introduction: The Meaning and Uses of Asymptotics | |
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| Consistency | |
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| First- and Higher-Order Asymptotics: The Delta Method with Applications | |
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| Asymptotic Theory in One Dimension | |
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| Asymptotic Behavior and Optimality of the Posterior Distribution | |
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| Inference in the Multiparameter Case | |
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| Inference for Gaussian Linear Models | |
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| Asymptotic Estimation Theory in p Dimensions | |
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| Large Sample Tests and Confidence Regions | |
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| Large Sample Methods for Discrete Data | |
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| Generalized Linear Models | |
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| Robustness Properties and Semiparametric Models | |
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| A Review of Basic Probability Theory | |
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| The Basic Model | |
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| Elementary Properties of Probability Models | |
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| Discrete Probability Models | |
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| Conditional Probability and Independence | |
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| Compound Experiments | |
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| Bernoulli and Multinomial Trials, Sampling with and without Replacement | |
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| Probabilities on Euclidean Space | |
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| Random Variables and Vectors: Transformations | |
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| Independence of Random Variables and Vectors | |
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| The Expectation of a Random Variable | |
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| Moments | |
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| Moment and Cumulant Generating Functions | |
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| Some Classical Discrete and Continuous Distributions | |
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| Modes of Convergence of Random Variables and Limit Theorems | |
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| Further Limit Theorems and Inequalities | |
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| Poisson Process | |
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| Additional Topics in Probability and Analysis | |
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| Conditioning by a Random Variable or Vector | |
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| Distribution Theory for Transformations of Random Vectors | |
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| Distribution Theory for Samples from a Normal Population | |
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| The Bivariate Normal Distribution | |
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| Moments of Random Vectors and Matrices | |
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| The Multivariate Normal Distribution | |
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| Convergence for Random Vectors:Opand Op Notation | |
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| Multivariate Calculus | |
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| Convexity and Inequalities | |
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| Topics in Matrix Theory and Elementary Hilbert Space Theory | |
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| Appendix C: Tables | |
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| The Standard Normal Distribution | |
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| Auxiliary Table of the Standard Normal Distribution | |
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| Distribution Critical Values | |
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| X 2 Distribution Critical Values | |
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| FDistribution Critical Values | |
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| Index | |