Goodness-of-fit test for partial functional linear model with errors in scalar covariates

In this article, we study the adequacy test of the partial functional linear model when the scalar predictors are measured with additive errors. Based on a corrected profile least-squares estimation of the null model, estimated residuals are first constructed, and a U-statistic-based test is proposed. The asymptotic properties of the test are investigated under the null and the alternative hypotheses. It is shown that the proposed test can control the type I error well, and its power performance is satisfactory. The finite sample performance of the proposed test is demonstrated through simulation studies and a real data analysis.