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<図書>
Stochastic processes : inference theory

責任表示 by M.M. Rao
シリーズ Mathematics and its applications ; v. 508
データ種別 図書
出版者 Dordrecht : Kluwer Academic Publishers
出版年 c2000
本文言語 英語
大きさ xvi, 645 p. ; 25 cm
概要 This book presents a complete mathematical treatment of classical inference theory (Neyman-Pearson, Fisher, and Wald) from the point of using it in stochastic processes, including some generalization.... It includes detailed analysis of likelihood ratios for both Gaussian and several other classes (infinitely divisible, jump Markov, diffusion and additive). Both linear and nonlinear filtering (also for general nonquadratic criteria) are treated. The corresponding Kalman-Bucy filters for continuous parameter processes are presented. Consistency and limit distributions of estimations of biospectral densities of harmonizable processes are given. Audience: Researchers and graduate students working in mathematics, statistics, and systems and communication engineering. 続きを見る
目次 Machine generated contents note: Chapter I: Introduction and Preliminaries 1
1.1 The problem of inference1
1.2 Testing a hypothesis4
1.3 Distinguishability of hypotheses7
1.4 Estimation of parameters10
1.5 Inference as a decision problem12
1.6 Complements and exercises15
Bibliographical notes17
Chapter II: Some Principles of Hypothesis Testing 19
2.1 Testing simple hypotheses19
2.2 Reduction of composite hypotheses38
2.3 Composite hypotheses with iterated weights42
2.4 Bayesian methodology for applications 48
2.5 Further results on composite hypotheses55
2.6 Complements and exercises67
Bibliographical notes70
Chapter III: Parameter Estimation and Asymptotics 73
3.1 Loss functions of different types 73
3.2 Existence and other properties of estimators75
3.3 Some principles of estimation 88
3.4 Asymptotics in estimation methodology107
3.5 Sequential estimation117
3.6 Complements and exercises125
Bibliographical notes130
Chapter IV: Inferences for Classes of Processes 133
4.1 Testing methods for second order processes133
4.2 Sequential testing of processes155
4.3 Weighted unbiased linear least squares prediction179
4.4 Estimation in discrete parameter models196
4.5 Asymptotic properties of estimators200
4.6 Complements and exercises213
Bibliographical notes219
Chapter V: Likelihood Ratios for Processes 223
5.1 Sets of admissible signals or translates223
5.2 General Gaussian processes247
5.3 Independent increment and jump Markov processes. 277
5.4 Infinitely divisible processes298
5.5 Diffusion type processes 314
5.6 Complements and exercises327
Bibliographical notes335
Chapter VI: Sampling Methods for Processes 339
6.1 Kotel'nikov-Shannon methodology339
6.2 Band limited sampling348
6.3 Analyticity of second order processes353
6.4 Periodic sampling of processes and fields358
6.5 Remarks on optional sampling374
6.6 Complements and exercises375
Bibliographical notes380
Chapter VII: More on Stochastic Inference 383
7.1 Absolute continuity of families of probability measures 383
7.2 Likelihood ratios for families of non Gaussian measures 405
7.3 Extension to two parameter families of measures413
7.4 Likelihood ratios in statistical communication theory 429
7.5 The general Gaussian dichotomy and Girsanov's theorem 435
7.6 Complements and exercises452
Bibliographical notes462
Chapter VIII: Prediction and Filtering of Processes 465
8.1 Predictors and projections465
8.2 Least squares prediction: the Cram6r-Hida approach 480
8.3 Linear filtering: Bochner's formulatioii488
8.4 Kalman-Bucy filters: the linear case/509
8.5 Kalman-Bucy filters: the nonlinear case535
8.6 Complements and exercises549
Bibliographical notes553
Chapter IX: Nonparametric Estimation for Processes 557
9.1 Spectra for classes of second order processes557
9.2 Asymptotically unbiased estimation of bispectra560
9.3 Resampling procedure and consistent estimation563
9.4 Associated spectral estimation for a class of processes 572
9.5 Limit distributions of (bi)spectral function estimators .583
9.6 Complements and exercises593
Bibliographical notes597
Bibliography 601
Notation index 627
Author index 633
Subject index 639.
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所蔵情報


理系図3F 数理独自 023212000002080 RAO,/40/5 2000

理系図 自動書庫 054212000001325 417.1/R 17/54000132 2000

書誌詳細

一般注記 Includes bibliography & index
著者標目 *Rao, M. M. (Malempati Madhusudana), 1929-
書誌ID 1001387798
ISBN 0792363248
NCID BA47023047
巻冊次 ISBN:0792363248
登録日 2009.11.02
更新日 2009.11.02