A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model Asghari, P.; Fakoor, V.; Sarmad, M.;
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 , 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 modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.
Asymptotic normality;Berry-Esseen;kernel density estimation;rate of convergence;left-truncation;
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