Kernel Based Estimation in Semiparametric Models with Missing at Random Responses

Abstract

Semiparametric regression models provide a powerful framework that combines the parametric and nonparametric paradigms, particularly effective for analyzing complex data structures. In practical scenarios, missing data is a pervasive issue that complicates statistical inference. This paper addresses semiparametric estimation when the response variable is subject to missingness under the Missing at Random (MAR) mechanism. We develop a kernel-based estimation strategy for the nonparametric component and employ partial regression methods—specifically, an adaptation of Robinson’s approach—to estimate the parametric part. The estimation procedure incorporates inverse probability weighting and nonparametric imputation to account for missing responses. Theoretical properties such as asymptotic bias, consistency, and variance are derived. The methodology is validated through two real-data analyses using the Abalone and Airfoil Self-Noise datasets, where missingness is artificially induced, demonstrating the effectiveness of the proposed strategy in preserving estimation accuracy. Our results underline the robustness and flexibility of semiparametric models in the presence of incomplete data.