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Parameter estimation and hypothesis testing in spectral analysis of stationary time series

Author: K O Dzhaparidze
Publisher: New York : Springer-Verlag, ©1986.
Series: Springer series in statistics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . , X , usually depends in n a complicated manner on the cyclic frequency).  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: K O Dzhaparidze
ISBN: 0387961410 9780387961415 3540961410 9783540961413
OCLC Number: 12583075
Notes: Translation of: Asimptoticheski ėffektivnoe ot︠s︡enivanie parametrov spektra gaussovskogo vremennogo ri︠a︡da.
Description: vi, 324 pages ; 25 cm.
Contents: I Properties of Maximum Likelihood Function for a Gaussian Time Series.- 1. General Expression for the log Likelihood.- 2. Asymptotic Expression for the "Principal Part" of the log Likelihood.- 3. The Asymptotic Differentiability of Gaussian Distributions with Spectral Densities Separated from Zero.- 4. The Asymptotic Differentiability of Gaussian Distributions with Spectral Densities Possessing Fixed Zeros.- Appendix 1.- Appendix 2.- Appendix 3. Remarks and Bibliography.- II Estimation of Parameters by Means of P. Whittle's Method.- 1. Asymptotic Maximum Likelihood Estimators.- 2. Properties of Asymptotic Maximum Likelihood Estimators in the Case of Strictly Positive Spectral Density.- 3. Consistency, Asymptotic Normality, and Asymptotic Efficiency of the Estimator $$\mathop \theta \limits^ \sim $$ in the Case of Spectral Density Possessing Fixed Zeros.- 4. Examples of Determination of Asymptotic Maximum Likelihood Estimators.- 5. Asymptotic Maximum Likelihood Estimator of the Spectrum of Processes Distorted by "White Noise".- 6. Least-Squares Estimation of Parameters of a Spectrum of a Linear Process.- 7. Estimation by Means of the Whittle Method of Spectrum Parameters of General Processes Satisfying the Strong Mixing Condition.- Appendix 1.- Appendix 2.- Appendix 3. Remarks and Bibliography.- III Simplified Estimators Possessing "Nice" Asymptotic Properties.- 1. Asymptotic Properties of Simplified Estimators.- 2. Examples of Preliminary Consistent Estimators.- 3. Examples of Constructing Simplified Estimators.- Appendix 1. Remarks and Bibliography.- IV Testing Hypotheses on Spectrum Parameters of a Gaussian Time Series.- 1. Testing Simple Hypotheses.- 2. Testing Composite Hypotheses (The Case of a Sequence of General "Asymptotically Differentiable Experiments").- 3. Testing of Composite Hypothesis about a Parameter of a Spectrum of a Gaussian Time Series.- Appendix 1. Remarks and Bibliography.- V Goodness-of-Fit Tests for Testing the Hypothesis about the Spectrum of Linear Processes.- 1. A Class of Goodness-of-Fit Tests for Testing a Simple Hypothesis about the Spectrum of Linear Processes.- 2. X2 Test for Testing a Simple Hypothesis about the Spectrum of a Linear Process.- 3. Goodness-of-Fit Test for Testing Composite Hypotheses about the Spectrum of a Linear Process.- Appendix 1. Remarks and Bibliography.
Series Title: Springer series in statistics.
Other Titles: Asimptoticheski ėffektivnoe ot︠s︡enivanie parametrov spektra gaussovskogo vremennogo ri︠a︡da.
Responsibility: K. Dzhaparidze ; translated by Samuel Kotz.

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