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Displaying similar documents to “Central limit theorem of the smoothed empirical distribution functions for asymptotically stationary absolutely regular stochastic processes.”

Extreme values and kernel estimates of point processes boundaries

Stéphane Girard, Pierre Jacob (2004)

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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.

Sojourn times.

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Journal of Applied Mathematics and Stochastic Analysis

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