🤖 AI Summary
This study addresses the semi-functional partially linear regression model with both finite-dimensional and functional covariates under randomly missing response data. It introduces, for the first time, the k-nearest neighbors (kNN) approach into this framework and proposes three kNN-based estimation strategies for the simultaneous estimation of finite-dimensional parameters and infinite-dimensional nonparametric operators. The proposed methodology offers a novel nonparametric modeling perspective for handling mixed-dimensional covariates with missing responses. Theoretically, the asymptotic consistency of the proposed estimators is rigorously established, demonstrating their feasibility and effectiveness in practical applications.
📝 Abstract
This paper considers a partial linear regression model with scalar response missing at random, one finite-dimensional covariate (a vector, $X$) and one infinite-dimensional covariate (a functional variable, $\mathcal{X}$). While the effect of $X$ on the response is linear, the effect of $\mathcal{X}$ is nonparametric. Three $k$NN-based estimators are proposed for both the vector parameter and the nonparametric operator, and some first asymptotic results are obtained.