Tail behaviour of Gaussian processes with applications to the Brownian pillow

Alex Koning and Vladimir Protassov

No EI 2001-49, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: In this paper we investigate the tail behaviour of a random variable S which may be viewed as a functional T of a zero mean Gaussian process X, taking special interest in the situation where X obeys the structure which is typical for limiting processes ocurring in nonparametric testing of [multivariate] indepencency and [multivariate] constancy over time. The tail behaviour of S is described by means of a constant a and a random variable R which is defined on the same probability space as S. The constant a acts as an upper bound, and is relevant for the computation of the efficiency of test statistics converging in distribution to S. The random variable R acts as a lower bound, and is instrumental in deriving approximations for the upper percentage points of S by simulation.

Keywords: Anderson-Darling type tests; Asymptotic distribution theory; Brownian pillow; Cramer-von Mises type tests; Gaussian processes; Kolmogorov type tests; Multivariate constancy; Multivariate independence; Tail behaviour (search for similar items in EconPapers)
Date: 2001-12-31
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Citations: View citations in EconPapers (2)

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