Local likelihood of quantile difference under left-truncated, right-censored and dependent assumptions

We, in this paper, focus on the inference of conditional quantile difference (CQD) for left-truncated and right-censored model. Based on local conditional likelihood function of the observed data, local likelihood ratio function and smoothed local log-likelihood ratio (log-SLL) of the CQD are constructed, and the maximum local likelihood estimator of the CQD is further defined from the log-SLL. When the observations are assumed to be a sequence of stationary alpha-mixing random variables, we establish asymptotic normality of the defined estimator, and prove the Wilks' theorem of adjusted log-SLL. Besides, we define another estimator of the CQD based on product-limit estimator of conditional distribution function and give its asymptotic normality. Also, simulation study and real data analysis are conducted to investigate the finite sample behaviour of the proposed methods.

Automated summary

In this paper, we focus on inferring the conditional quantile difference (CQD) for a left-truncated and right-censored model. We construct the local conditional likelihood function, the local likelihood ratio function, and the smoothed local log-likelihood ratio (log-SLL) of the CQD based on the observed data. Furthermore, we define the maximum local likelihood estimator of the CQD from the log-SLL. We establish the asymptotic normality of the defined estimator under the assumption of a sequence of stationary alpha-mixing random variables and prove the Wilks' theorem of adjusted log-SLL. Additionally, we define another estimator of the CQD based on the product-limit estimator of the conditional distribution function and provide its asymptotic normality. We also conduct simulation studies and real data analysis to examine the finite sample behavior of the proposed methods.