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Erscheinungsjahr: 
2025
Quellenangabe: 
[Journal:] Statistical Papers [ISSN:] 1613-9798 [Volume:] 66 [Issue:] 6 [Article No.:] 135 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2025
Verlag: 
Springer, Berlin, Heidelberg
Zusammenfassung: 
Finding the eigenvalues connected to the covariance operator of a centered Hilbert-space valued Gaussian process is genuinely considered a hard problem in several mathematical disciplines. In Statistics this problem arises for instance in the asymptotic null distribution of goodness-of-fit test statistics of weighted -type as well as in the limit distribution of degenerate U -statistics. For this problem we present the Rayleigh–Ritz method to approximate the eigenvalues. The usefulness of these approximations is shown by high lightening implications such as critical value approximation and theoretical comparison of test statistics by means of Bahadur efficiencies.
Schlagwörter: 
Covariance operator
Eigenvalues
Rayleigh-Ritz method
Gaussian Processes
Statistics
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