A uniform functional law of the logarithm for the local empirical process

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We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estimators.
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000243

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Probability, 60F05, 60F15, 62E20, 62G30 (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/72770

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410143
 http://arxiv.org/abs/math/0410143
 Annals of Probability 2004, Vol. 32, No. 2, 1391-1418
 doi:10.1214/009117904000000243

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arXiv