A sequence of independent nonnegative random variables with common distribution function $F$ is censored on the right by another sequence of independent identically distributed random variables. These two sequences are also assumed to be independent. We estimate the density function $f$ of $F$ by a sequence of kernel estimators $f_n(t) = (\int^\infty_{-\infty}K((t - x)/h(n))d\hat{F}_n(x))/h(n),$ where $h(n)$ is a sequence of numbers, $K$ is kernel density function and $\hat{F}_n$ is the product-limit estimator of $F.$ We prove central limit theorems for $\int^T_0|f_n(t) - f(t)|^p d\mu(t), 1 \leq p < \infty, 0 < T \leq \infty,$ where $\mu$ is a measure on the Borel sets of the real line. The result is tested in Monte Carlo trials and applied for goodness of fit.
Publié le : 1991-12-14
Classification:
Censored data,
kernel estimator,
$L_1$ norm,
Wiener process,
strong approximation,
60F05,
62G10,
60G15
@article{1176348372,
author = {Csorgo, Miklos and Gombay, Edit and Horvath, Lajos},
title = {Central Limit Theorems for $L\_p$ Distances of Kernel Estimators of Densities Under Random Censorship},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 1813-1831},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348372}
}
Csorgo, Miklos; Gombay, Edit; Horvath, Lajos. Central Limit Theorems for $L_p$ Distances of Kernel Estimators of Densities Under Random Censorship. Ann. Statist., Tome 19 (1991) no. 1, pp. 1813-1831. http://gdmltest.u-ga.fr/item/1176348372/