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Stationary sequences and random fields

Author: Murray Rosenblatt
Publisher: Boston : Birkhäuser, 1985.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This dis- cussion allows one to get results on the asymptotic distribution of finite para- meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of  Read more...

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Genre/Form: Stationäre Folge
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Murray Rosenblatt
ISBN: 0817632646 9780817632649 3764332646 9783764332648
OCLC Number: 11133630
Language Note: English.
Description: 258 pages ; 24 cm
Contents: I Stationary Processes.- 1. General Discussion.- 2. Positive Definite Functions.- 3. Fourier Representation of a Weakly Stationary Process.- Problems.- Notes.- II Prediction and Moments.- 1. Prediction.- 2. Moments and Cumulants.- 3. Autoregressive and Moving Average Processes.- 4. Non-Gaussian Linear Processes.- 5. The Kalman-Bucy Filter.- Problems.- Notes.- III Quadratic Forms, Limit Theorems and Mixing Conditions.- 1. Introduction.- 2. Quadratic Forms.- 3. A Limit Theorem.- 4. Summability of Cumulants.- 5. Long-range Dependence.- 6. Strong Mixing and Random Fields.- Problems.- Notes.- IV Estimation of Parameters of Finite Parameter Models.- 1. Maximum Likelihood Estimates.- 2. The Newton-Raphson Procedure and Gaussian ARMA Schemes.- 3. Asymptotic Properties of Some Finite Parameter Estimates.- 4. Sample Computations Using Monte Carlo Simulation.- 5. Estimating the Order of a Model.- 6. Finite Parameter Stationary Random Fields.- Problems.- V Spectral Density Estimates.- 1. The Periodogram.- 2. Bias and Variance of Spectral Density Estimates.- 3. Asymptotic Distribution of Spectral Density Estimates.- 4. Prewhitening and Tapering.- 5. Spectral Density Estimates Using Blocks.- 6. A Lower Bound for the Precision of Spectral Density Estimates.- 7. Turbulence and the Kolmogorov Spectrum.- 8. Spectral Density Estimates for Random Fields.- Problems.- Notes.- VI Cumulant Spectral Estimates.- 1. Introduction.- 2. The Discrete Fourier Transform and Fast Fourier Transform.- 3. Vector-Valued Processes.- 4. Smoothed Periodograms.- 5. Aliasing and Discretely Sampled Time Series.- Notes.- VII Density and Regression Estimates.- 1. Introduction. The Case of Independent Observations.- 2. Density and Regression Estimates for Stationary Sequences.- Notes.- VIII Non-Gaussian Linear Processes.- 1. Estimates of Phase, Coefficients, and Deconvolution for Non-Gaussian.- Linear Processes.- 2. Random Fields.- 3. Non-Gaussian Linear Random Fields.- Notes.- 1. Monotone Functions and Measures.- 2. Hilbert Space.- 3. Banach Space.- 4. Banach Algebras and Homomorphisms.- Postscript.- Author Index.
Responsibility: Murray Rosenblatt.

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