ASYMPTOTIC NORMALITY OF THE DECONVOLUTION KERNEL DENSITY ESTIMATORS BASED ON INDEPENDENT AS WELL AS STRONG MIXING RIGHT CENSORED DATA

Abstract

We consider estimation of a density when observed lifetime from the convolution model contaminated by additive measurement errors. A kernel type deconvolution density estimator of the unknown distribution based on right censored data is proposed by using the Inverse-Probability-of-Censoring Weighted Average. Further, we discuss the asymptotic normality of the deconvolution kernel density estimators for independent and strong mixing vectors when the error distribution function is either ordinary smooth or supersmooth. Our method is applied to the study conducted by UTSW medical center. The research team at UTSW collected the data of women who underwent cystoscopy fulguration for recurrent urinary tract infection (UTI) from 2004-2016. Using the estimators and the asymptotic distributions of the estimators, we estimate the survival probability of the time from infection to recurrent UTI.