Nonparametric modal regression with mixed variables and application to analyze the GDP data

Abstract

Modal regression is as efficient as mean regression when the random error follows normal distribution, and is robust to the presence of outliers or skewed distributions. Due to such advantages as efficiency and robustness, it has been widely applied in different fields, such as medicine, economics, environment and so on. However, most existing literature based on modal regression are assumed that the covariates are continuous, but discrete variable is very common in practice. In this paper, inspired by the idea of modal regression, an adaptive estimation procedure is proposed for nonparametric models with mixed discrete and continuous regressors. Under some mild assumptions, the limiting behavior of the proposed approach can be established, and a simply feasible estimation algorithm is provided in practice. To illustrate the performance of our proposed method, some numerical results are presented in simulation part. Finally, the proposed method is applied to analyze the GDP data of OECD and non-OECD countries.