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Tail behaviour of Gaussian processes with applications to the Brownian pillow

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  • Koning, A.J.
  • Protassov, V.

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 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.

Suggested Citation

  • Koning, A.J. & Protassov, V., 2001. "Tail behaviour of Gaussian processes with applications to the Brownian pillow," Econometric Institute Research Papers EI 2001-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:591
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    References listed on IDEAS

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    1. 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.
    2. Hjort, N.L. & Koning, A.J., 2001. "Constancy of distributions: nonparametric monitoring of probability distributions over time," Econometric Institute Research Papers EI 2001-50, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Samorodnitsky, Gennady, 1991. "Probability tails of Gaussian extrema," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 55-84, June.
    4. 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.
    5. 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.
    6. Kallenberg, Wilbert C. M. & Koning, Alex J., 1995. "On Wieand's theorem," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 121-132, November.
    7. De Wet, T., 1980. "Cramér-von Mises tests for independence," Journal of Multivariate Analysis, Elsevier, vol. 10(1), pages 38-50, March.
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    Cited by:

    1. Hjort, N.L. & Koning, A.J., 2001. "Constancy of distributions: nonparametric monitoring of probability distributions over time," Econometric Institute Research Papers EI 2001-50, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Koning, A.J. & Hjort, N.L., 2002. "Constancy of distributions: asymptotic efficiency of certain nonparametric tests of constancy," Econometric Institute Research Papers EI 2002-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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