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Quantative bounds for high-dimensional non-linear functionals of Gaussian processes

Ponente: David Kramer-Bang
Institución: The University of Warwick
Tipo de Evento: Investigación, Formación de Recursos Humanos

Cuándo 05/02/2025
de 17:00 a 18:00
Dónde Salón de Seminarios S-104, Facultad de Ciencias
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Título: Quantative bounds for high-dimensional non-linear functionals of Gaussian processes

Resumen: Explicit quantitative bounds in the hyper-rectangle distance d_HR in terms of a Berry-Esseen type bound are derived, in the setting of high-dimensional, non-linear functionals of Gaussian processes while allowing for a strong dependence structure. Under some smoothness and regularity assumptions, the rate under d_HR is determined to be sub-polynomial in dimension d and, in the case where the underlying Gaussian process has short-range dependence, the dependence on the number of observations n is found to be n^{-1/2}log(n). Many statistical applications arise, where important examples covered in the paper are; method of moments, empirical characteristic functions, empirical moment-generating functions and a functional Breuer-Major theorem.