This $440,000 National Science Foundation project grant under the Mathematical and Physical Sciences program (CFDA 47.049) will support the development of modal regression models for abnormal data analysis. The principal investigator at the University of California, Riverside will develop a suite of new parametric and nonparametric modal regression techniques as an alternative to traditional mean and quantile regression models. This involves imposing assumptions on the conditional mode of a dependent variable given covariates to estimate the most probable value rather than the mean or quantiles. An expectation-maximization algorithm and studies of estimator properties are also included. Software for implementing the new modal regression methods will be made publicly available. The results will benefit researchers analyzing skewed, truncated or heterogeneous data common in fields like economics, social sciences, medicine, biology and agriculture.