Statistical inference of high-dimensional factor-adjusted partially linear regression models
摘要
In this paper, we propose a high-dimensional factor-adjusted sparse partially linear regression model that integrates the linear effects of high-dimensional, significantly correlated covariates with the nonparametric effects of low-dimensional covariates. The proposed framework combines the interpretability of linear models, the flexibility of nonparametric modeling and the ability to effectively account for dependence among high-dimensional predictors. We develop a penalized estimation procedure that incorporates B-spline approximation and factor analysis, and establish error bounds for the resulting estimators. To facilitate valid inference for the linear component, we further propose a factor-adjusted projection-debiased procedure and employ a Gaussian multiplier bootstrap to obtain critical values. Theoretical guarantees are derived under suitable regularity conditions. Extensive simulation studies demonstrate the favorable finite-sample performance of the proposed method. An application to a birth weight dataset, which serves as the motivating example, further illustrates its effectiveness and practical usefulness.