统计学实验及决策、渐进理论STATISTICAL EXPERIMENTS AND DECISION, ASYMPTOTIC THEORY mobi 下载 网盘 caj lrf pdf txt 阿里云

This volume provides an exposition of some fundamental ***ects of the asymptotic theory of statistical experiments. The most important of them is "how to c***truct asymptotically optimal decisi*** if we know the structure of optimal decisi*** 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 Transformati***

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 Reas*** for Introducing the λ-Convergence

2.4 λ-Convergence（Definition，Examples）

2.5 λ-Convergence and Accompanying Experiments

2.6 Uniform Versi*** 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 Decisi*** and Estimators

2.10 Proof of Lemma about“Rec***truction”

2.11 Expansi*** 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 Definiti***

4.2 Asymptotic Minimax Theorems under Local λ-Convergence

4.3 Global Estimation. Preliminary C***iderati***

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 aut***ression

5.2.3 Non-Gaussian errors: explosive aut***ression

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 Conditi***

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