左截断数据下非线性模型的加权分位数回归

左截断数据是一类具有特殊结构的缺失数据,当且仅当研究变量大于一定的阈值时才能取得观察值.本文针对左截断数据下的非线性回归模型,提出了加权分位数估计方法,利用加权方式处理左截断缺失数据,取得了与完整数据相近的估计结果.并在一定假设条件下,证明了所提估计方法的一致性和渐近正态性等大样本性质,最后通过数值模拟展现所提估计方法的有限样本表现.

A Weighted Quantile Regression for Nonlinear Models with Left Truncated Data

Left truncated data is a type of missing data with a special structure that can only be obtained if the study variable is greater than a certain threshold.In this paper,the weighted quantile regression estimation method is proposed for the nonlinear regression model with left truncated data.The left truncated data is processed by weighted method,and the estimation results are similar to those obtained by complete data.Under certain assumptions,it is shown that the proposed estimator is strongly consistent and asymptotically normal.Finally,the finite sample performance of the proposed method is demonstrated by numerical simulation.