A Computationally Efficient Method for Estimating Semi Parametric Regression Functions

Bias reduction is an important condition for effective feature extraction. Utilizing recent theoretical results in high dimensional statistical modeling, we propose a model-free yet computationally simple approach to estimate the partially linear model Y = Xβ+g(Z)+ε. Based on partitioning the support of Z, a simple local average is used to approximate the response surface g(Z). The model can be estimated via least squares and no tuning parameter is needed. The proposed method seeks to strike a balance between computation burden and efficiency of the estimators while minimizing model bias. The desired theoretical properties of the proposed estimators are established. Moreover, since the proposed method bypasses data-driven bandwith selection of traditional nonparametric methods, it avoids the further efficiency loss due to computation burden.