Estimators Of Smooth Quantile Differences With Left-truncated And Right-censored Data

In the deta analysis,often encounter the problems of rright censored and left truncated deta.Which have much important applications in survival analysis,medicat.statistics,astronomy,economics and engineering reliability statistics.This paper,based on the left truncated right censored data,the bit difference function is calculated using the product limit estimation method,and the smooth quantile difference and the empirical quantile difference estimation are calculated.The losses proposed by Hodges and Lehmann(1970)are used as the criteria for comparing the two estimation efficiency.Compared with the kernel quantile estimation,the relative deficit of the quantile estimation of LTRC data is studied.The product limit estimation is proposed,the product limit estimation is smooth,and the smooth quantile difference estimation based on the product limit estimation is obtained.The numerical simulation method is obtained by comparing the efficiency of the smooth quantile difference and the empirical quantile difference estimation by the deficit.The quantile difference is verified.The programming software used in this paper is R language.The specific steps of the study are as follows:first,the left truncated right censored data is generated according to the correlation index distribution.Then,the bit difference function is calculated by the product limit estimation,and the smooth quantile difference and the empirical quantile difference estimation are calculated.Finally,the smooth quantile difference and experience are compared with the deficit and the experience.The left truncated right censored data of different sample sizes is generated by the correlation model model,and the efficiency of the estimation of the smooth quantile difference and the empirical quantile difference is compared by the deficit,The efficiency of the quantile difference estimation is verified by numerical simulation.The key problem to be solved is to compare the efficiency of the smooth quantile difference and the empirical quantile difference estimation by the deficit.so as to determine whether the smooth partition potential difference estimation is effective.