Confidence Interval Construction For Quantile Residual Lifetime Under Left-truncated And Right-censored Data

Recently,censored data has aroused wide concern in quantile residual lifetime.In the clinical trials,data are often censored and truncated at the same time.In this paper,we discuss the construction of confidence intervals for the remaining life quantiles mainly based on the left-truncated and right-censored data.The traditional method of confidence interval construction usually is not ideal,and the variance of estimator is quite complicated on small sample.So we study the construction of confidence intervals.Jackknife-d is one of the most commonly used resampling method,which make full use of auxiliary information of interested and also estimate variance for non-smooth variable with some advantages,such as unbiased.On the other hand,Bootstrap-t is also a kind of important non-parameter method.which construct the confidence interval directly from the data information without any theoretical assumptions and also showed good coverage error in the interval construction even for small sample.Therefore,the method of Jackknife-d and the Bootstrap-t are used to construct the confidence interval of quantile residual lifetime under the left-truncated and right-censored data in the paper and asymptotic properties of estimators are given respectively.At the same time,we asses four traditional kinds of interval estimation method and two resample method through examples and monte carlo simulation.Simulation results show that under the condition of small samples,the proposed two kinds of resampling method has obvious advantage than the traditional methods in the interval length.And the Jackknife-d method makes the shortest length,which is a kind of very good confidence interval estimation method.