Titre du document / Document title

The law of the iterated logarithm for the multivariate nearest neighbor density estimators

Auteur(s) / Author(s)

RALESCU S. S. ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

City univ. New York, Queens coll., ETATS-UNIS

Résumé / Abstract

We consider estimation of a multivariate probability density function f(x) by kernel type nearest neighbor (nn) estimators g_n(x). The development of nn density estimation theory has had a rich history since Loftsgaarden and Quesenberry proposed the idea in 1965. In particular, there is a vast literature on convergence properties of g_n(x) to f(x). For statistical purposes, however, it is of importance to study also the speed of almost sure convergence. For pointwise estimation, this problem appears to have received no attention in the literature. The aim of the present paper is to obtain sharp pointwise rates of strong consistency by establishing a law of the iterated logarithm for this class of estimators. We also study the local estimation of a density function based on censored data by the kernel smoothing method using a nearest neighbor approach and derive a law of the iterated logarithm

Revue / Journal Title

Journal of multivariate analysis   ISSN 0047-259X   CODEN JMVAAI 

Source / Source

1995, vol. 53, n^o1, pp. 159-179 (29 ref.)

Langue / Language

Anglais

Editeur / Publisher

Elsevier, San Diego, CA, ETATS-UNIS  (1971) (Revue)

Mots-clés anglais / English Keywords

Law of iterated logarithm ; Order statistic ; Multivariate distribution ; Probability density function ; Nearest neighbour ; Convergence speed ; Almost sure convergence ; Data smoothing ; Estimator ;

Mots-clés français / French Keywords

Loi logarithme itéré ; Statistique ordre ; Loi n variables ; Fonction densité probabilité ; Plus proche voisin ; Vitesse convergence ; Convergence presque sûre ; Lissage données ; Estimateur ;

Mots-clés espagnols / Spanish Keywords

Ley logaritmo iterado ; Estadística orden ; Ley n variables ; Función densidad probabilidad ; Vecino más cercano ; Velocidad convergencia ; Convergencia casi segura ; Alisadura datos ; Estimador ;

Localisation / Location

INIST-CNRS, Cote INIST : 15722, 35400005653127.0100