Partially adaptive econometric methods for regression and classification

Abstract

Assumptions about the distributions of domain variables are important for much of statistical learning, including both regression and classification problems. However, it is important that the assumed models are consistent with the stylized facts. For example selecting a normal distribution permits modeling two data characteristics-the mean and the variance, but it is not appropriate for data which are skewed or have thick tails. The adaptive methods developed here offer the flexibility found in many machine learning models, but lend themselves to statistical interpretation, as well. This paper contributes to the development of partially adaptive estimation methods that derive their adaptability from membership in families of distributions, which are distinguished by modifications of simple parameters. In particular, we have extended the methods to include recently proposed distributions, including example applications and computational details