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Strong representation of the presmoothed quantile function estimator for censored data
Author(s) -
Jácome M. A.,
Cao R.
Publication year - 2008
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2008.00388.x
Subject(s) - quantile function , quantile , estimator , mathematics , asymptotic distribution , consistency (knowledge bases) , consistent estimator , statistics , nonparametric statistics , econometrics , minimum variance unbiased estimator , probability distribution , moment generating function , discrete mathematics
We consider lifetime data subject to right random censorship. In this context, this paper deals with the topic of estimating the distribution function of the lifetime and the corresponding quantile function. As it has been shown that the classical Kaplan–Meier estimator of the distribution function can be improved by means of presmoothing ideas, we introduce a quantile function estimator via the presmoothed distribution function estimator studied by Cao et al. [ Journal of Nonparametric statistics , Vol. 17 (2005) pp. 31–56.] The main result of this paper is an almost sure representation of this presmoothed estimator. As a consequence, its strong consistency and asymptotic normality are established. The performance of this new quantile estimator is analyzed in a simulation study and applied to a real data example.