Bahadur–Kiefer representations for time dependent quantile processes

Kevei, Péter and Mason, David M. (2018) Bahadur–Kiefer representations for time dependent quantile processes. PERIODICA MATHEMATICA HUNGARICA, 76 (1). pp. 95-113. ISSN 0031-5303

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Abstract

We define a time dependent empirical process based on n independent fractional Brownian motions and describe strong approximations to it by Gaussian processes. They lead to strong approximations and functional laws of the iterated logarithm for the quantile or inverse of this empirical process. They are obtained via time dependent Bahadur–Kiefer representations.

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