Abstract
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.
Citation
Miklos Csorgo. Edit Gombay. Lajos Horvath. "Central Limit Theorems for $L_p$ Distances of Kernel Estimators of Densities Under Random Censorship." Ann. Statist. 19 (4) 1813 - 1831, December, 1991. https://doi.org/10.1214/aos/1176348372
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