基于光滑化方法的分段线性删失分位数回归模型估计

The Piecewise Linear Censored Quantile Regression Model Estimation Based on Smoothing Technique

针对在分段线性删失分位数回归模型中的变点问题,该文通过引入光滑化方法得到了变点位置及模型系数的估计,推导了参数估计的大样本性质.光滑化方法解决了在变点估计方法中常用的格点搜索法存在计算烦琐、解释意义不强的问题,弥补了线性化技术无法证明渐近性的不足,提高了估计的有效性和稳健性.蒙特卡罗模拟结果验证了在同方差和异方差、固定和随机删失下在不同分位点时的估计效果都具有有效性和稳健性.药物滥用数据的实证分析表明:复发时间间隔与治疗时间存在正向影响,且复发时间在0.498处存在变点(0.5分位数),治疗时间在0.498之前的复发时间间隔比在0.498之后的更长,即大约前一半时间的治疗更加有效.

The smoothing technique is proposed in the piecewise linear censored quantile regression model to solve the problem of change point,the estimator of change point and coefficients are obtained,and the large sample properties of the estimator is derived.The smoothing technique solves the cumbersome calculation and unreal meaning of the grid search method,and remedies the difficulty that linearization technology cannot prove the asymptotic properties.The validity and robustness of the estimation are verified by Monte Carlo simulation with homoscedasticity and heteroscedasticity,fixed and random censoring at different quantiles.The empirical analysis of drug abuse data shows that the recurrence interval and treatment time have a positive effect,and the recurrence time has a change point at 0.498(0.5 quantile).The treatment time before 0.498 is longer than after 0.498,that is,the treatment in the first half of the time is more effective.