Displaying similar documents to “Sums of extreme values of subordinated long-range dependent sequences: moving averages with finite variance.”

Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries

Ludovic Menneteau (2008)

ESAIM: Probability and Statistics

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In this paper, we give sufficient conditions to establish central limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided. ...

Goodness-of-fit test for long range dependent processes

Gilles Fay, Anne Philippe (2002)

ESAIM: Probability and Statistics

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In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodness-of-fit test for long-range dependent processes. Our test statistic is performed in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic distribution of our statistic under the null hypothesis. Under specific alternative hypotheses, we prove that the power converges to one. The performance of our test procedure is...

Extreme values and kernel estimates of point processes boundaries

Stéphane Girard, Pierre Jacob (2004)

ESAIM: Probability and Statistics

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We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.

Chover-type laws of the iterated logarithm for weighted sums of NA sequences

Guang-hui Cai (2007)

Mathematica Bohemica

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To derive a Baum-Katz type result, a Chover-type law of the iterated logarithm is established for weighted sums of negatively associated (NA) and identically distributed random variables with a distribution in the domain of a stable law in this paper.