Modal Regression Estimation for Heteroscedastic Single-Index Model

The single-index model is a semi-parametric regression model that avoids the curse of dimensionality because of the linear combination of p-regression coefficients and covariates. Most of the works in this setting done for the homogenous single index models are limited and based on the minimum average conditional variance estimation (MAVE). To overcome these drawbacks, in this paper, we provide a robust and efficient estimate with modal regression for the single-index model under the existence of heteroscedasticity. The EM algorithm and bandwidth selection are employed to prepare the estimation method. Simulation studies demonstrate the performance of the proposed estimation; this method outperforms MAVE in various situations even if the errors are generated from a heavy-tailed distribution while it achieves the same efficiency as well as MAVE for the normally distributed errors. Finally, the application of the proposed method is illustrated by a real example of the heteroscedastic model.