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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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    1. De Wet, T., 1980. "Cramér-von Mises tests for independence," Journal of Multivariate Analysis, Elsevier, vol. 10(1), pages 38-50, March.
    2. Csörgo, Miklós, 1979. "Strong approximations of the Hoeffding, Blum, Kiefer, Rosenblatt multivariate empirical process," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 84-100, March.
    3. Deheuvels, Paul, 1981. "An asymptotic decomposition for multivariate distribution-free tests of independence," Journal of Multivariate Analysis, Elsevier, vol. 11(1), pages 102-113, March.
    4. Samorodnitsky, Gennady, 1991. "Probability tails of Gaussian extrema," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 55-84, June.
    5. Kallenberg, Wilbert C. M. & Koning, Alex J., 1995. "On Wieand's theorem," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 121-132, November.
    6. Cotterill Derek S. & Csörgö Miklós, 1985. "On The Limiting Distribution Of And Critical Values For The Hoeffding, Blum, Kiefer, Rosenblatt Independence Criterion," Statistics & Risk Modeling, De Gruyter, vol. 3(1-2), pages 1-48, February.
    7. Eastwood, Brian J. & Eastwood, Vera R., 1992. "Percentiles for Cramér-von Mises functionals of Gaussian processes and some applications to Bayesian tests," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 329-344, September.
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    Cited by:

    1. Enkelejd Hashorva, 2010. "Boundary Non-crossings of Brownian Pillow," Journal of Theoretical Probability, Springer, vol. 23(1), pages 193-208, March.
    2. 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.

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