Empirical distribution function for mixing random variables. application in nonparametric hazard estimation
作者:
P. Sarda,
P. Vieu,
期刊:
Statistics
(Taylor Available online 1989)
卷期:
Volume 20,
issue 4
页码: 559-571
ISSN:0233-1888
年代: 1989
DOI:10.1080/02331888908802207
出版商: Akademie-Verlag
关键词: GLIVENKO-CANTELLI theorem;empirical distribution function;hazard function;density;φ;-mixing;kernel estimates
数据来源: Taylor
摘要:
Let X be a multivariate random variable and (Xn)Na 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 (Xn). 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
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