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Some extremal problems for Gaussian and Empirical random fields

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  • A.I. Nazarov
  • Ya.Yu. Nikitin

Abstract

Some important problems of probability and statistics can be reduced to the evaluation of supremum of some homogeneous functional defined on the Strasses ball in the space of smooth functions on the square. We give the solution of this extremal problem in two particular cases: when the functional is linear and continuous and when it is a superposition of two seminorms. As a result we obtain the rough large deviation asymptotic for Lp-norms of Brownian fields on the square, some Strassen type laws of iterated logarithm for functional of Brownian fields, and describe the conditions of local Bahadur optimality for some nonparametric independence tests such as generalized rank correlation coefficients.

Suggested Citation

  • A.I. Nazarov & Ya.Yu. Nikitin, 2000. "Some extremal problems for Gaussian and Empirical random fields," ICER Working Papers 22-2000, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpicer:22-2000
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2000/Nikitin222000.pdf
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    References listed on IDEAS

    as
    1. Bajorski, Piotr, 1987. "Local bahadur optimality of some rank tests of independence," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 255-262, June.
    2. Ledwina, Teresa, 1986. "On the limiting Pitman efficiency of some rank tests of independence," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 265-271, December.
    3. Park, W. J., 1974. "On Strassen's version of the law of the iterated logarithm for the two-parameter Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 4(4), pages 479-485, December.
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    Cited by:

    1. Henze, Norbert & Nikitin, Yakov & Ebner, Bruno, 2009. "Integral distribution-free statistics of Lp-type and their asymptotic comparison," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3426-3438, July.

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