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\iteman{io-port 04126494}
\itemau{Sarda, P.; Vieu, P.}
\itemti{Empirical distribution function for mixing random variables. Application in nonparametric hazard estimation.}
\itemso{Statistics 20, No.4, 559-571 (1989).}
\itemab
Summary: Let $X$ be a multivariate random variable and $(X\sb n)\sb N$ a sequence of realizations of $X$ which are not necessarily assumed to be independent. We derive a generalization of Glivenko-Cantelli theorem under a $\phi$-mixing condition on the sequence $(X\sb n)$. This result together with an improvement of the uniform rate of convergence on a compact set of density kernel estimates leads to uniform rate of convergence of hazard kernel estimates. This last result is illustrated by means of Monte Carlo experiments.
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\itemut{dependence structure; consistency; empirical distribution function; hazard function; phi-mixing; density estimation; multivariate random variable; generalization of Glivenko-Cantelli theorem; uniform rate of convergence; compact set of density kernel estimates; hazard kernel estimates}
\itemli{doi:10.1080/02331888908802207}
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