Integral Least-Squares Inferences for Semiparametric Models with Functional Data

Abstract

The inferences for semiparametric models with functional data are investigated. We propose an integral least-squares technique for estimating the parametric components, and the asymptotic normality of the resulting integral least-squares estimator is studied. For the nonparametric components, a local integral least-squares estimation method is proposed, and the asymptotic normality of the resulting estimator is also established. Based on these results, the confidence intervals for the parametric component and the nonparametric component are constructed. At last, some simulation studies and a real data analysis are undertaken to assess the finite sample performance of the proposed estimation method.