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.

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
Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus School of Economics

Koning, A.J, & Protassov, V. (2001). Tail behaviour of Gaussian processes with applications to the Brownian pillow (No. EI 2001-49). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from