Robust estimation for the varying coefficient partially nonlinear models

In this paper, we propose a robust estimation procedure based on the exponential squared loss (ESL) function for the varying coefficient partially nonlinear model. Under some conditions, the asymptotic properties of proposed estimators are established. Furthermore, we develop a new minorization-maximization (MM) algorithm to calculate the estimates for both non-parametric and parametric parts, and introduce a data-driven procedure to select the tuning parameters. Simulation studies illustrate that the proposed method is more robust and efficient than the classical least squares technique when there are outliers in the dataset. Finally, we apply the proposed methodology to analyze a real dataset. The results reveal that the proposed has better the predictive ability.