Functional Partial Linear Regression with Autoregressive Errors

This paper investigates a functional partial linear model with autoregressive errors, where the relationship between functional predictor and the scalar response is linear, while the scalar predictor is nonparametric. We first approximate the functional regression parameter and nonparametric function by two given B-spline basis, respectively. Then, we estimate the spline coefficients by a weighted least square method. In the presented paper, we derive the theoretical properties including the convergence rate of the functional regression parameter and the nonparametric function estimate for the scalar predictor. Furthermore, we illustrate the performance of the proposed method by simulation studies and one real data analysis.