A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

Title & Authors
A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model
Asghari, P.; Fakoor, V.; Sarmad, M.;

Abstract
In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $\small{Y{\geq}T}$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $\small{n^{-1/6}}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.
Keywords
Asymptotic normality;Berry-Esseen;kernel density estimation;rate of convergence;left-truncation;
Language
English
Cited by
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