عنوان

Gaussian and Non-Gaussian Linear Time Series and Random Fields

شابک

9781461212621

شابک

9781461270676

شماره

b402720

عنوان اصلي

Gaussian and Non-Gaussian Linear Time Series and Random Fields

نام عام مواد

[Book]

نام نخستين پديدآور

by Murray Rosenblatt.

محل نشرو پخش و غیره

New York, NY :

نام ناشر، پخش کننده و غيره

Imprint: Springer,

تاریخ نشرو بخش و غیره

2000.

عنوان فروست

Springer Series in Statistics,

شاپا ي ISSN فروست

0172-7397

متن يادداشت

1 Reversibility and Identifiability -- 1.1 Linear Sequences and the Gaussian Property -- 1.2 Reversibility -- 1.3 Identifiability -- 1.4 Minimum and Nonminimum Phase Sequences -- 2 Minimum Phase Estimation -- 2.1 The Minimum Phase Case and the Quasi-Gaussian Likelihood -- 2.2 Consistency -- 2.3 The Asymptotic Distribution -- 3 Homogeneous Gaussian Random Fields -- 3.1 Regular and Singular Fields -- 3.2 An Isometry -- 3.3 L-Fields and L-Markov Fields -- 4 Cumulants, Mixing and Estimation for Gaussian Fields -- 4.1 Moments and Cumulants -- 4.2 Higher Order Spectra -- 4.3 Some Simple Inequalities and Strong Mixing -- 4.4 Strong Mixing for Two-Sided Linear Processes -- 4.5 Mixing and a Central Limit Theorem for Random Fields -- 4.6 Estimation for Stationary Random Fields -- 4.7 Cumulants of Finite Fourier Transforms -- 4.8 Appendix: Two Inequalities -- 5 Prediction for Minimum and Nonminimum Phase Models -- 5.1 Introduction -- 5.2 A First Order Autoregressive Model -- 5.3 Nonminimum Phase Autoregressive Models -- 5.4 A Functional Equation -- 5.5 Entropy -- 5.6 Continuous Time Parameter Processes -- 6 The Fluctuation of the Quasi-Gaussian Likelihood -- 6.1 Initial Remarks -- 6.2 Derivation -- 6.3 The Limiting Process -- 7 Random Fields -- 7.1 Introduction -- 7.2 Markov Fields and Chains -- 7.3 Entropy and a Limit Theorem -- 7.4 Some Illustrations -- 8 Estimation for Possibly Nonminimum Phase Schemes -- 8.1 The Likelihood for Possibly Non-Gaussian Autoregressive Schemes -- 8.2 Asymptotic Normality -- 8.3 Preliminary Comments: Approximate Maximum Likelihood Estimates for Non-Gaussian Nonminimum Phase ARMA Sequences -- 8.4 The Likelihood Function -- 8.5 The Covariance Matrix -- 8.6 Solution of the Approximate Likelihood Equations -- 8.7 Cumulants and Estimation for Autoregressive Schemes -- 8.8 Superefficiency -- Bibliographic Notes -- References -- Notation -- Author Index.

بدون عنوان

0

متن يادداشت

Much of this book is concerned with autoregressive and moving av erage linear stationary sequences and random fields. These models are part of the classical literature in time series analysis, particularly in the Gaussian case. There is a large literature on probabilistic and statistical aspects of these models-to a great extent in the Gaussian context. In the Gaussian case best predictors are linear and there is an extensive study of the asymptotics of asymptotically optimal esti mators. Some discussion of these classical results is given to provide a contrast with what may occur in the non-Gaussian case. There the prediction problem may be nonlinear and problems of estima tion can have a certain complexity due to the richer structure that non-Gaussian models may have. Gaussian stationary sequences have a reversible probability struc ture, that is, the probability structure with time increasing in the usual manner is the same as that with time reversed. Chapter 1 considers the question of reversibility for linear stationary sequences and gives necessary and sufficient conditions for the reversibility. A neat result of Breidt and Davis on reversibility is presented. A sim ple but elegant result of Cheng is also given that specifies conditions for the identifiability of the filter coefficients that specify a linear non-Gaussian random field.

شماره استاندارد بين المللي کتاب و موسيقي

9781461270676

عنوان

Springer eBooks

موضوع مستند نشده

Distribution (Probability theory).

موضوع مستند نشده

Mathematical statistics.

موضوع مستند نشده

Statistics.

مستند نام اشخاص تاييد نشده

Rosenblatt, Murray.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190301082400.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y