Robust Estimation for Semi-Functional Linear Model with Autoregressive Errors

Abstract

It is well-known that the traditional functional regression model is mainly based on the least square or likelihood method. These methods usually rely on some strong assumptions, such as error independence and normality, that are not always satisfied. For example, the response variable may contain outliers, and the error term is serially correlated. Violation of assumptions can result in unfavorable influences on model estimation. Therefore, a robust estimation procedure of a semi-functional linear model with autoregressive error is developed to solve this problem. We compare the efficiency of our procedure to the least square method through a simulation study and two real data analyses. The conclusion illustrates that the proposed method outperforms the least square method, providing random errors follow the heavy-tail distribution.