因变量缺失下部分线性可加模型的估计和检验（英文）

Estimation and Testing for Partially Linear Additive Model with Missing Responses at Random

本文研究部分线性可加模型在因变量存在缺失情形下的统计推断问题.首先基于完整数据方法提出了参数分量的Profile最小二乘估计并证明估计量的渐近正态性.为了给出参数分量的区间估计,构造了渐近分布为卡方分布的经验似然统计量.为了检验参数分量的线性约束条件,构造了调整的广义似然比检验统计量,当原假设成立时其渐近分布为卡方分布,从而将广义似然比检验推广到了缺失数据情形.最后通过数值模拟验证所提方法的有效性.

This paper considers statistical inference for the partially linear additive model with missing responses at random. We propose a profile least-squares estimator for the parametric component with complete-case data, and show that the resulting estimator is asymptotically normal. To construct a confidence region for the parametric component, we propose an empirical-likelihood-based statistic, which is shown to have a chi-squared distribution asymptotically. To check the validity of the linear constraints on the parametric component, we construct a modified generalized likelihood ratio to test statistic and to demonstrate that it follows asymptotically chi-squared distribution under the null hypothesis. Then, we extend the generalized likelihood ratio technique to the context of missing data. F^rthermore, simulation study is conducted to illustrate the performance of the proposed methods.