Tail behaviour of Gaussian processes with applications to the Brownian pillow
AbstractIn this paper we investigate the tail behaviour of a random variable S which maybe viewed as a functional T of a zero mean Gaussian process X, taking specialinterest in the situation where X obeys the structure whichis 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 aand a random variable R which is defined on the same probability spaceas S.The constant a acts as an upper bound, and is relevant for the computation ofthe efficiency of test statistics converging in distribution to S. The random variable R acts as a lower bound, andis instrumental in deriving approximations for the upper percentage points of S by simulation.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2001-49.
Date of creation: 31 Dec 2001
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Anderson-Darling type tests; Asymptotic distribution theory; Brownian pillow; Cramer-von Mises type tests; Gaussian processes; Kolmogorov type tests; Multivariate constancy; Tail behaviour; Multivariate independence;
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