Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/330529 
Year of Publication: 
2025
Citation: 
[Journal:] Statistical Papers [ISSN:] 1613-9798 [Volume:] 66 [Issue:] 6 [Article No.:] 135 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2025
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
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.
Subjects: 
Covariance operator
Eigenvalues
Rayleigh-Ritz method
Gaussian Processes
Statistics
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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