Doubly robust and efficient estimation in a partially linear multiple-index model
提出一种部分线性多指标模型，通过新损失函数构建估计方程，实现回归参数的双重稳健有效估计，并构造非参数函数的局部线性估计，模拟和实际数据验证了方法有效性。
In this paper, we introduce a partially linear multiple-index model. A new loss function is proposed to set up a general class of estimating equations to obtain the doubly robust and efficient estimation of the regression parameters. The estimators of the nonparametric functions are also constructed via local linear fitting. The asymptotic properties of the proposed estimators are proved. Furthermore, the bias-corrected empirical log-likelihood ratios of the regression parameters are proposed. It is shown that the proposed ratios are asymptotically standard chi-squared, and the obtained results can be directly used to construct the confidence regions of the regression parameters. Simulation studies and real data analysis show that the proposed method is effective.