Tail behaviour of Gaussian processes with applications to the Brownian pillow

Alex J. Koning and Vladimir Protasov

Journal of Multivariate Analysis, 2003, vol. 87, issue 2, 370-397

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 occurring in nonparametric testing of (multivariate) independency 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 approximation for the upper percentage points of S by simulation.

Keywords: Tail; behaviour; Gaussian; processes; Brownian; pillow; Asymptotic; distribution; theory; Kolmogorov-type; tests; Cramer-von; Mises; type; tests; Anderson-Darling-type; tests; Multivariate; constancy; Multivariate; independence (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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