kNN estimation in semi-functional partial linear regression with missing responses at random

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.