عنوان

Asymptotic statistical methods for stochastic processes /

(Number (ISBN

0821811835 (alk. paper)

(Number (ISBN

9780821811832 (alk. paper)

Number

dltt

Title Proper

Asymptotic statistical methods for stochastic processes /

General Material Designation

[Book]

First Statement of Responsibility

Yu. N. Linʹkov.

Place of Publication, Distribution, etc.

Providence, RI :

Name of Publisher, Distributor, etc.

American Mathematical Society,

Date of Publication, Distribution, etc.

c2001.

Specific Material Designation and Extent of Item

xvi, 216 p. :

Other Physical Details

ill. ;

Dimensions

26 cm.

Series Title

Translations of mathematical monographs,

Volume Designation

v. 196

ISSN of Series

0065-9282 ;

Text of Note

Includes bibliographical references and index.

Text of Note

Ch. 1. Local Densities of Measures and Limit Theorems for Stochastic Processes. 1.1. Basic notions of the theory of stochastic processes. 1.2. Statistic experiments generated by stochastic processes. 1.3. Limit theorems for semimartingales -- Ch. 2. Asymptotic Distinguishing between Simple Hypotheses in the Scheme of General Statistical Experiments. 2.1. Statistical hypotheses and tests. 2.2. Types of asymptotic distinguishability between families of hypotheses and their characterization. 2.3. Complete asymptotic distinguishability under the conditions of the law of large numbers. 2.4. Complete asymptotic distinguishability under conditions of weak convergence. 2.5. Contiguous families of hypotheses. 2.6. The case of asymptotic expansion of the likelihood ratio. 2.7. Reduction of the problem of testing hypotheses -- Ch. 3. Asymptotic Behavior of the Likelihood Ratio in Problems of Distinguishing between Simple Hypotheses for Semimartingales. 3.1. Hellinger integrals and Hellinger processes. 3.2. Limit theorems for the likelihood ratio. 3.3. Asymptotic decomposition of the likelihood ratio in parametric formulation. 3.4. Observations of diffusion-type processes. 3.5. Observations of counting processes -- Ch. 4. Asymptotic Estimation of Parameters. 4.1. Formulation of the problem. 4.2. Properties of the normalized likelihood ratio for semimartingales. 4.3. Observations of diffusion-type processes. 4.4. Observations of counting processes -- Ch. 5. Asymptotic Information-Theoretic Problems in Parameter Estimation. 5.1. Asymptotic behavior of the Shannon information in observations with respect to an unknown parameter. 5.2. Lower bounds for the information about a statistical estimate of a parameter. 5.3. Bounds for risk functions of consistent estimates. 5.4. Observations of semimartingales.

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General Material Designation

Asimptoticheskie metody statistiki sluchaĭnykh protÍŁsessov.

Language (when part of a heading)

English

Mathematical statistics-- Asymptotic theory.

Semimartingales (Mathematics)

Class number

Book number

LinÊ£kov, IÍŁU. N.

Date of Transaction

20140220044133.0

Electronic name

[Book]

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