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Title: On approximating eigenvalues of covariance operators with applications to goodness-of-fit tests Authors:  Bruno Ebner - Karlsruhe Institute of Technology (Germany) [presenting]
Bojana Milosevic - University of Belgrade (Serbia)
Maria Dolores Jimenez-Gamero - Universidad de Sevilla (Spain)
Abstract: Methods are reviewed to approximate eigenvalues of covariance operators connected to limiting Gaussian processes. We present a new method to approximate the largest eigenvalue connected to the Rayleigh-Ritz method and apply it to limit distributions of statistics of weighted $L^2$ type in several goodness-of-fit settings of distribution-free type or classical testing problems as testing for exponentiality or normality. Finally, we apply the methods in different settings and show the impact on efficiency statements of the asymptotic Bahadur type.