Robust estimation for varying coefficient partially functional linear regression models based on exponential squared loss function

Abstract

In this article, we present a new robust estimation procedure based on the exponential squared loss function for varying coefficient partially functional linear regression models, where the slope function and nonparametric coefficients are approximated by functional principal component basis functions and B splines, respectively. Under some mild conditions, the convergence rates of the resulted estimators are obtained. Simulation studies indicate that our proposed method can achieve robustness against outliers or heavy-tail error distributions and perform no worse than the popular least-squares estimation method for the normal error case. Finally, a real data example is used to illustrate the application of the proposed method.

Keywords

• exponential squared loss function
• varying coefficient partially functional linear regression models
• robustness
• convergence rates
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