Gaussian and Non-Gaussian Linear Time Series and Random Fields
By: by Murray Rosenblatt
Series: Springer Series in Statistics; Springer series in statistics
Publisher: Springer New York
Published: 2000
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 247
ISBN-13: 9781461270676; 9781461212621
Subjects: Distribution (Probability theory); Statistics; Mathematical statistics
Description: The book is concerned with linear time series and random fields in both the Gaussian and especially the non-Gaussian context. The principal focus is on autoregressive moving average models and analogous random fields. Probabilistic and statistical questions are both discussed. The Gaussian models are contrasted with noncausal or noninvertible (nonminimum phase) non-Gaussian models which can have a much richer structure than Gaussian models. The book deals with problems of prediction (which can have a nonlinear character) and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. The book is intended as a text for graduate students in statistics, mathematics, engineering, the natural sciences and economics. An initial background in probability theory and statistics is suggested. Notes on background, history and open problems are given at the end of the book. Murray Rosenblatt is Professor of Mathematics at the University of California, San Diego. He was a Guggenheim Fellow in 1965 and 1972 and is a member of the National Academy of Sciences, U.S.A. He is the author of Random Processes (1962), Markov Processes: Structure and Asymptotic Behavior (1971), Stationary Sequences and Random Fields (1985), and Stochastic Curve Estimation (1991).
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Table of contents: title: Reversibility and Identifiability; title: Minimum Phase Estimation; title: Homogeneous Gaussian Random Fields; title: Cumulants, Mixing and Estimation for Gaussian Fields; title: Prediction for Minimum and Nonminimum Phase Models; title: The Fluctuation of the quasi-Gaussian Likelihood; title: Random Fields; title: Estimation for Possibly Nonminimum Phase Schemes.