Test for High-Dimensional Regression Coeffcients in Partially Functional Linear Models

In practical applications, functional and high-dimensional data are often observed simultaneously. The partially functional linear model is a powerful tool for handling this type of mixed data. In this paper, we develop a U test statistic to discuss the overall test for high-dimensional regression coeffcients in partially functional linear models. With the aid of the martingale central limit theorem, we derive the asymptotic distributions of the proposed test under the null hypothesis and local alternative hypothesis. We examine the finite-sample performance of the proposed test via Monte Carlo simulations, which show that the new test performs well both in size and power. We also demonstrate the effectiveness and application through an empirical analysis of an air pollution data set.