统计学实验及决策、渐进理论STATISTICAL EXPERIMENTS AND DECISION, ASYMPTOTIC THEORY fb2 免费 lrf 下载 kindle azw3 pdf 阿里云

This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is "how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment".

Prface

Chapter1 Statistical Experiments and Their Comparisom

1.1 Statistical Experiment

1.2 Randomiztion of SDtperiment

1.3 Examples of Comparisom of Experiment.I

1.4 The Main Components of the General Decision Theory

1.5 Randomiztion of Statistiacl Experiments.II. General case

1.6 Comparison of Experiments via Decision Problems

1.7 Deficiencyδ（ε.ε） and Δ-DistanceΔ（ε.ε*）

1.8 On Calculation of Deficiency δ（ε.ε）and△Distance

1.9 Some Explicit Formulas of Comparison of Experiments

1.10 A Particular Case of Comparison of Experiments

1.11 The Hellinger and Mellin Transformations

1.12 Absolutely Continuous and Comtiguous Probability Measurse

Chapter2 Comvergence of Statistical Experiments

2.1 Strong（Δ-）Convergence

2.2 Weak（ω-）Convergence

2.3 Reasons for Introducing the λ-Convergence

2.4 λ-Convergence（Definition，Examples）

2.5 λ-Convergence and Accompanying Experiments

2.6 Uniform Versions of λ-Convergence

2.7 λ（κ）-Convergence and Asymptotic Minimax Theorems

2.8 Comparison of Various Kinds of Convergence

2.9 Convergence of Statistical Decisions and Estimators

2.10 Proof of Lemma about“Reconstruction”

2.11 Expansions for Likelihood

2.12 Extended λ-Convergence

2.13 Contiguity of Statistical Experimenst.Ⅰ

2.14 Contiguity of Statistical Experimenst.Ⅱ

Chapter3 （γ，Γ）-Modele. Convergence to（γ，Γ）-Models

3.1 Definition of（γ，Γ）-Models. Examples

3.2 Generalized Bayes Approach of（γ，Γ）-Models. Examples

3.3 Lower Bound of minimax Risk of（γ，Γ）-Models. Examples

3.4 Structure of Regular Extistical Experiments to （γ，Γ）-Models. Examples

3.5 λ-Convergence of Statistical Experiments

3.6 Approximation by（γ，Γ；*）-Modes.Ⅰ

3.7 Approximation by（γ，Γ；*）-Modes.Ⅱ

Chapter4 Local Convergence of Dtatistical Experiments and Global Extimation

4.1 Localλ-Convergence. main Definitions

4.2 Asymptotic Minimax Theorems under Local λ-Convergence

4.3 Global Estimation. Preliminary Considerations

4.4 Connectedness Equation for LocalλConvergence

4.5 Asymptotic Efficiency of Global Estimators

4.6 Connectedness Equation for Transitive Experiments

4.7 Global Estimation for Transitive Limit Experiments

Chapter5 Statistical Inference for Autoregressive Models of the First Order

5.1 Parameter Estimation

5.2 Convergence of Statistical Experiments

5.2.1 Gaussian errors

5.2.2 Non-Gaussian errors: stable autorgression

5.2.3 Non-Gaussian errors: explosive autorgression

5.3 Asymptotic Efficient Minimax Estimation

5.3.1 Gaussian case. Lower bounds

5.3.2 Gaussian case. Upper bounds

5.3.3 Non-Gaussian case

5.4 Sequential Estimation

Bibliography

Index

List of Symbols

List of Conditions

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