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<図書>
Asymptotic statistical methods for stochastic processes

責任表示 Yu. N. Linʹkov ; [translated from the Russian by Victor Kotov]
シリーズ Translations of mathematical monographs ; v. 196
データ種別 図書
出版者 Providence, R.I. : American Mathematical Society
出版年 c2001
本文言語 英語
大きさ xvi, 216 p. : 26 cm
概要 Introduces local densities of probability measures generated by semimartingales, and investigates their asymptotic properties for various types of asymptotic distinguishability of the corresponding fa...ilies of statistical hypotheses. Certain problems of simple hypothesis testing and estimation of an unknown parameter from observation of semimartingales, as well as some asymptotic information-theoretic problems of statistics, are then solved. Originally published in Russian in 1993. Annotation copyrighted by Book News, Inc., Portland, OR続きを見る
目次 Machine generated contents note: Chapter 1. Local Densities of Measures and Limit Theorems for Stochastic
Processes 1
1.1. Basic notions of the theory of stochastic processes 1
1.2. Statistic experiments generated by stochastic processes 9
1.3. Limit theorems for semimartingales 21
Chapter 2. Asymptotic Distinguishing between Simple Hypotheses in the
Scheme of General Statistical Experiments 33
2.1. Statistical hypotheses and tests 33
2.2. Types of asymptotic distinguishability between families of hypothe-
ses and their characterization 36
2.3. Complete asymptotic distinguishability under the conditions of the
law of large numbers 45
2.4. Complete asymptotic distinguishability under conditions of weak
convergence 52
2.5. Contiguous families of hypotheses 58
2.6. The case of asymptotic expansion of the likelihood ratio 65
2.7. Reduction of the problem of testing hypotheses 70
Chapter 3. Asymptotic Behavior of the Likelihood Ratio in Problems of
Distinguishing between Simple Hypotheses for Semimartingales 79
3.1. Hellinger integrals and Hellinger processes 79
3.2. Limit theorems for'the likelihood ratio 83
3.3. Asymptotic decomposition of the likelihood ratio in parametric
formulation 88
3.4. Observations of diffusion-type processes 98
3.5. Observations of counting processes 112
Chapter 4. Asymptotic Estimation of Parameters 137
4.1. Formulation of the problem 137
4.2. Properties of the normalized likelihood ratio for semimartingales 140
4.3. Observations of diffusion-type processes 151
4.4. Observations of counting processes 156
Chapter 5. Asymptotic Information-Theoretic Problems in Parameter Es-
timation 161
5.1. Asymptotic behavior of the Shannon information in observations
with respect to an unknown parameter 161
5.2. Lower bounds for the information about a statistical estimate of a
parameter 174
5.3. Bounds for risk functions of consistent estimates 186
5.4. Observations of semimartingales 194
Bibliographical Notes 197
References 203
Index 213.
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所蔵情報


理系図3F 数理独自 023212000007826 LINK/10/1 2001

理系図3F 数理独自 023212001007714 LINK/10/1A 2001

書誌詳細

別書名 ローマ字翻字タイトル:Asimptoticheskie metody statistiki sluchaĭnykh prot︠s︡essov
原タイトル:Асимптотические методы статистики случайных процессов
一般注記 Includes bibliographical references (p. 203-212) and index
著者標目 *Linʹkov, I︠U︡. N.
件 名 LCSH:Mathematical statistics -- Asymptotic theory  全ての件名で検索
LCSH:Semimartingales (Mathematics)
分 類 LCC:QA276
DC21:519.5
書誌ID 1001387070
ISBN 0821811835
NCID BA4969222X
巻冊次 ISBN:0821811835
登録日 2009.11.02
更新日 2009.11.02

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