Goodness-of-Fit Tests for Stationary Gaussian Processes with Tapered Data

The paper is concerned with the construction of goodness-of-fit tests for testing a hypothesis H 0 that the hypothetical spectral density of a stationary Gaussian process X ( t ) has the specified form, based on the tapered data. We show that in the case where the hypothetical spectral density of X...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2021-02, Vol.171 (1), Article 1
Main Author: Ginovyan, Mamikon S.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Chi-square test
Computational Mathematics and Numerical Analysis
Constraining
Density
Gaussian process
Goodness of fit
Hypotheses
Mathematics
Mathematics and Statistics
Parameter estimation
Partial Differential Equations
Probability Theory and Stochastic Processes
Spectra
Statistical tests
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Summary:The paper is concerned with the construction of goodness-of-fit tests for testing a hypothesis H 0 that the hypothetical spectral density of a stationary Gaussian process X ( t ) has the specified form, based on the tapered data. We show that in the case where the hypothetical spectral density of X ( t ) does not depend on unknown parameters (the hypothesis H 0 is simple), then the suggested test statistic has a limiting chi-square distribution. In the case where the hypothesis H 0 is composite, that is, the hypothetical spectral density of X ( t ) depends on an unknown parameter, we choose an appropriate estimator for unknown parameter and describe the limiting distribution of the test statistic. This distribution is similar to that of obtained by Chernov and Lehman (Ann. Math. Stat. 25(3):579–586, 1954 ) in the case of independent observations.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-020-00368-0