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Tail behaviour of Gaussian processes with applications to the Brownian pillow

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  • Koning, Alex J.
  • Protasov, Vladimir

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.

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  • Koning, Alex J. & Protasov, Vladimir, 2003. "Tail behaviour of Gaussian processes with applications to the Brownian pillow," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 370-397, November.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:370-397
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    Cited by:

    1. Koning, A.J. & Franses, Ph.H.B.F., 2003. "Did the incidence of high precipitation levels increase? Statistical evidence for the Netherlands," Econometric Institute Research Papers EI 2003-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Enkelejd Hashorva, 2010. "Boundary Non-crossings of Brownian Pillow," Journal of Theoretical Probability, Springer, vol. 23(1), pages 193-208, March.

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