Modal Regression for Skewed, Truncated, or Contaminated Data with Outliers

Built on the ideas of mean and quantile, mean regression and quantile regression are extensively investigated and popularly used to model the relationship between a dependent variable Y  and covariates x. However, the research about the regression model built on the mode is rather limited. In this article, we introduce a new regression tool, named modal regression, that aims to find the most probable conditional value (mode) of a dependent variable Y  given covariates x rather than the mean that is used by the traditional mean regression. The modal regression can reveal new interesting data structure that is possibly missed by the conditional mean or quantiles. In addition, modal regression is resistant to outliers and heavy-tailed data and can provide shorter prediction intervals when the data are skewed. Furthermore, unlike traditional mean regression, the modal regression can be directly applied to the truncated data. Modal regression could be a potentially very useful regression tool that can complement the traditional mean and quantile regressions.