Empirical distribution function for mixing random variables. application in nonparametric hazard estimation

1 January 1989

journal article
research article
Published by Taylor & Francis in Statistics

Vol. 20 (4) , 559-571
https://doi.org/10.1080/02331888908802207

Abstract

Let X be a multivariate random variable and (X_n)_N a sequence of realisations of X which are not necessarily assumed to be independent. We derive a generalization of GLIVENKO-CANTELLI theorem under a φ-mixing,condition on the sequence (X_n). This result together with an improvement of the uniform rate of convergence on a compact set of density kernel estimate leads to uniform rate of convergence of hazard kernel estimate. This last result is illustrated by means of Monte Carlo experiments

Keywords

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