Eigenvalues approximation of integral covariance operators with applications to weighted $L^2$ statistics
<|reference_start|>Eigenvalues approximation of integral covariance operators with applications to weighted $L^2$ statistics: Finding the eigenvalues connected to the covariance operator of a centred 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 $L^2$-type. 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.<|reference_end|>
@article{ebner2024eigenvalues,
    title={Eigenvalues approximation of integral covariance operators with
  applications to weighted $L^2$ statistics},
    author={Bruno Ebner and Mar'ia Dolores Jim'enez-Gamero and Bojana
  Milov{s}evi'c},
    journal={arXiv preprint arXiv:2408.08064},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.08064},
    primaryClass={math.ST cs.NA math.NA stat.TH}
}