Stochastic processes
Subtitle: inference theory
By: by M.M. Rao.
Series: Mathematics and its applications -- v. 508; Mathematics and its applications (Kluwer Academic Publishers) -- v. 508.
Publisher: Kluwer Academic Publishers
Published: 2000
Place of publication: Dordrecht; Boston
Language: eng
Number of pages: 645
Subjects: Stochastic processes.; Mathematical statistics.
Notes: Includes bibliographical references (p. 601-625) and indexes.
Table of contents: title: Machine generated contents note: Chapter I: Introduction and Preliminaries 1; title: 1.1 The problem of inference1; title: 1.2 Testing a hypothesis4; title: 1.3 Distinguishability of hypotheses7; title: 1.4 Estimation of parameters10; title: 1.5 Inference as a decision problem12; title: 1.6 Complements and exercises15; title: Bibliographical notes17; title: Chapter II: Some Principles of Hypothesis Testing 19; title: 2.1 Testing simple hypotheses19; title: 2.2 Reduction of composite hypotheses38; title: 2.3 Composite hypotheses with iterated weights42; title: 2.4 Bayesian methodology for applications 48; title: 2.5 Further results on composite hypotheses55; title: 2.6 Complements and exercises67; title: Bibliographical notes70; title: Chapter III: Parameter Estimation and Asymptotics 73; title: 3.1 Loss functions of different types 73; title: 3.2 Existence and other properties of estimators75; title: 3.3 Some principles of estimation 88; title: 3.4 Asymptotics in estimation methodology107; title: 3.5 Sequential estimation117; title: 3.6 Complements and exercises125; title: Bibliographical notes130; title: Chapter IV: Inferences for Classes of Processes 133; title: 4.1 Testing methods for second order processes133; title: 4.2 Sequential testing of processes155; title: 4.3 Weighted unbiased linear least squares prediction179; title: 4.4 Estimation in discrete parameter models196; title: 4.5 Asymptotic properties of estimators200; title: 4.6 Complements and exercises213; title: Bibliographical notes219; title: Chapter V: Likelihood Ratios for Processes 223; title: 5.1 Sets of admissible signals or translates223; title: 5.2 General Gaussian processes247; title: 5.3 Independent increment and jump Markov processes. 277; title: 5.4 Infinitely divisible processes298; title: 5.5 Diffusion type processes 314; title: 5.6 Complements and exercises327; title: Bibliographical notes335; title: Chapter VI: Sampling Methods for Processes 339; title: 6.1 Kotel'nikov-Shannon methodology339; title: 6.2 Band limited sampling348; title: 6.3 Analyticity of second order processes353; title: 6.4 Periodic sampling of processes and fields358; title: 6.5 Remarks on optional sampling374; title: 6.6 Complements and exercises375; title: Bibliographical notes380; title: Chapter VII: More on Stochastic Inference 383; title: 7.1 Absolute continuity of families of probability measures 383; title: 7.2 Likelihood ratios for families of non Gaussian measures 405; title: 7.3 Extension to two parameter families of measures413; title: 7.4 Likelihood ratios in statistical communication theory 429; title: 7.5 The general Gaussian dichotomy and Girsanov's theorem 435; title: 7.6 Complements and exercises452; title: Bibliographical notes462; title: Chapter VIII: Prediction and Filtering of Processes 465; title: 8.1 Predictors and projections465; title: 8.2 Least squares prediction: the Cram6r-Hida approach 480; title: 8.3 Linear filtering: Bochner's formulatioii488; title: 8.4 Kalman-Bucy filters: the linear case/509; title: 8.5 Kalman-Bucy filters: the nonlinear case535; title: 8.6 Complements and exercises549; title: Bibliographical notes553; title: Chapter IX: Nonparametric Estimation for Processes 557; title: 9.1 Spectra for classes of second order processes557; title: 9.2 Asymptotically unbiased estimation of bispectra560; title: 9.3 Resampling procedure and consistent estimation563; title: 9.4 Associated spectral estimation for a class of processes 572; title: 9.5 Limit distributions of (bi)spectral function estimators .583; title: 9.6 Complements and exercises593; title: Bibliographical notes597; title: Bibliography 601; title: Notation index 627; title: Author index 633; title: Subject index 639.