基于双侧截断的部分线性回归模型的参数估计

Parametric Estimation for Partial Linear Models with Double Truncated Data

摘要: 受实验观测时长或观测条件导致的数据双侧截断在生存分析等领域十分常见，故而对该类数据在不同适用模型下的讨论具有研究意义。考虑双侧截断数据下的部分线性模型，针对观测到数据的逆概率加权，利用核估计对模型线性部分参数给出估计，并给出估计量的偏差与方差的渐进表达式，与常见的模型参数估计方法相比估计值偏差与标准差有一定程度的提升且更准确。通过数值模拟和AIDS病毒感染年龄与潜伏期的相关数据，验证了该方法的实用性。

Abstract: Double truncated data due to the limit of observing time and other objective reasons of the experiments are quite common in the field of survival analysis. So the discussion of this type of data under different models is of great significance. Considering the partial linear model under the two-sided truncated data, based on the inverse probability weighting of the observed data, kernel estimation is used to estimate the linear parameter. Asymptotic expressions for the bias and variance of the estimator are given. Compared with the common method, the bias and variance are improved. The real data analysis of AIDS virus infection age and incubation proves the practicability of the proposed method.