Advanced Statistical Science and Applied Probability

Asymptotic Theory

By: SHIRYAEV A N

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Hardcover | 5 July 2000

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300 Pages

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24.41 x 16.99 x 1.75

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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".

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"It is an interesting, welcome addition to the literature, and it contains many new insights. I congratulate the authors for writing this comprehensive monograph on a difficult subject." Mathematical Reviews, 2001

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Preface
Statistical Experiments and Their Comparison	p. 1
Statistical Experiment	p. 1
Randomization of Statistical Experiment. I	p. 10
Examples of Comparison of Experiments	p. 13
The Main Components of the General Decision Theory	p. 16
Randomization of Statistical Experiments. II. General case	p. 22
Comparison of Experiments via Decision Problems	p. 25
Deficiency [delta]([epsilon], [epsilon]) and [Delta]-Distance [Delta] ([epsilon],[epsilon])	p. 28
On Calculation of Deficiency [delta]([epsilon],[epsilon]) and [Delta]-Distance	p. 38
Some Explicit Formulas for Deficiency and [Delta]-Distance	p. 41
A Particular Case of Comparison of Experiments	p. 48
The Hellinger and Mellin Transformations	p. 49
Absolutely Continuous and Contiguous Probability Measures	p. 57
Convergence of Statistical Experiments	p. 61
Strong ([Delta]-) Convergence	p. 61
Weak ([omega]-) Convergence	p. 68
Reasons for Introducing the [lambda]-Convergence	p. 72
[lambda]-Convergence (Definition, Examples)	p. 76
[lambda]-Convergence and Accompanying Experiments	p. 83
Uniform Versions of [lambda]-Convergence	p. 88
[lambda]([Kappa])-Convergence and Asymptotic Minimax Theorems	p. 92
Comparison of Various Kinds of Convergence	p. 102
Convergence of Statistical Decisions and Estimators	p. 107
Proof of Lemma about "Reconstruction"	p. 111
Expansions for Likelihood	p. 116
Extended [lambda]-Convergence	p. 121
Contiguity of Statistical Experiments. I	p. 125
Contiguity of Statistical Experiments. II	p. 128
([gamma],[Gamma])-Models. Convergence to ([gamma],[Gamma])-Models	p. 135
Definition of ([gamma],[Gamma])-Models. Examples	p. 135
Generalized Bayes Approach for ([gamma],[Gamma])-Models	p. 144
Lower Bound of Minimax Risk for ([gamma],[Gamma])-Models	p. 156
Structure of Regular Estimators for Some ([gamma],[Gamma])-Models	p. 162
[lambda]-Convergence of Statistical Experiments to ([gamma],[Gamma])-Models	p. 164
Approximation by ([gamma],[Gamma];[psi])-Models. I	p. 166
Application by ([gamma],[Gamma];[psi])-Models. II	p. 173
Local Convergence of Statistical Experiments and Global Estimation	p. 179
Local [lambda]-Convergence. Main Definitions	p. 179
Asymptotic Minimax Theorems under Local [lambda]-Convergence	p. 182
Global Estimation. Preliminary Considerations	p. 188
Connectedness Equation for Local [lambda]-Convergence	p. 193
Asymptotic Efficiency of Global Estimators	p. 204
Connectedness Equation for Transitive Experiments	p. 211
Global Estimation for Transitive Limit Experiments	p. 218
Statistical Inference for Autoregressive Models of the First Order	p. 223
Parameter Estimation	p. 223
Convergence of Statistical Experiments	p. 237
Asymptotic Efficient Minimax Estimation	p. 246
Sequential Estimation	p. 254
Bibliography	p. 269
Index	p. 277
List of Symbols	p. 279
List of Conditions	p. 283
Table of Contents provided by Blackwell. All Rights Reserved.

Advanced Statistical Science and Applied Probability

Asymptotic Theory

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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