Resumen
Explicit quantitative bounds in the hyper-rectangle distance dHR in terms of a Berry-Esseen type bound are derived, in the setting of highdimensional, non-linear functionals of Gaussian processes while allowing for a strong dependence structure. Under some smoothness and regularity assumptions, the rate under dHR 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-1/2log(n). Many statistical applications arise, where important examples covered in the paper are; method of empirical characteristic functions, empirical moment-generating functions and a functional Brever-Major.
Ponente
David Kramer-Bang
UNIVERSITY OF WARWICK
Informes
seminarioproba@matem.unam.mx
https://www.matem.unam.mx/-seminarioproba/
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