Theory of Point Estimation

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E. L. Lehmann, G. Casella

Chapter 1Preparations[173/0%]

Section 1.1The Problem[13/0%]

Section 1.2Measure Theory and Integration[11/0%]

Section 1.3Probability Theory[8/0%]

Section 1.4Group Families[16/0%]

Section 1.5Exponential Families[33/0%]

Section 1.6Sufficient Statistics[38/0%]

Section 1.7Convex Loss Functions[27/0%]

Section 1.8Convergence in Probability and in Law[27/0%]

Chapter 2Unbiasedness[136/0%]

Section 2.1UMVU Estimators[22/0%]

Section 2.2Continuous One- and Two-Sample Problems[29/0%]

Section 2.3Discrete Distributions[30/0%]

Section 2.4Nonparametric Families[10/0%]

Section 2.5The Information Inequality[33/0%]

Section 2.6The Multiparameter Case and Other Extensions[12/0%]

Chapter 3Equivariance[155/0%]

Section 3.1First Examples[22/0%]

Section 3.2The Principle of Equivariance[28/0%]

Section 3.3Location-Scale Families[42/0%]

Section 3.4Normal Linear Models[21/0%]

Section 3.5Random and Mixed Effects Models[17/0%]

Section 3.6Exponential Linear Models[8/0%]

Section 3.7Finite Population Models[17/0%]

Chapter 4Average Risk Optimality[116/0%]

Section 4.1Introduction[12/0%]

Section 4.2First Examples[16/0%]

Section 4.3Single-Prior Bayes[12/0%]

Section 4.4Equivariant Bayes[14/0%]

Section 4.5Hierarchical Bayes[21/0%]

Section 4.6Empirical Bayes[21/0%]

Section 4.7Risk Comparisons[20/0%]

Chapter 5Minimaxity and Admissibility[164/0%]

Section 5.1Minimax Estimation[33/0%]

Section 5.2Admissibility and Minimaxity in Exponential Families[25/0%]

Section 5.3Admissibility and Minimaxity in Group Families[15/0%]

Section 5.4Simultaneous Estimation[14/0%]

Section 5.5Shrinkage Estimators in the Normal Case[25/0%]

Section 5.6Extensions[20/0%]

Section 5.7Admissibility and Complete Classes[32/0%]

Chapter 6Asymptotic Optimality[169/0%]

Section 6.1Performance Evaluations in Large Samples[39/0%]

Section 6.2Asymptotic Efficiency[14/0%]

Section 6.3Efficient Likelihood Estimation[29/0%]

Section 6.4Likelihood Estimation: Multiple Roots[19/0%]

Section 6.5The Multiparameter Case[6/0%]

Section 6.6Applications[17/0%]

Section 6.7Extensions[34/0%]

Section 6.8Asymptotic Efficiency of Bayes Estimators[11/0%]