Robust Discovery of Regression Models

Abstract

Successful modeling of observational data requires jointly discovering the determinants of the underlying process and the observations from which it can be reliably estimated, given the near impossibility of pre-specifying both. To do so requires avoiding many potential problems, including substantive omitted variables; unmodeled non-stationarity and misspecified dynamics in time series; non-linearity; and inappropriate conditioning assumptions, as well as incorrect distributional shape combined with contaminated observations from outliers and shifts. The aim is to discover robust, parsimonious representations that retain the relevant information, are well specified, encompass alternative models, and evaluate the validity of the study. An approach is proposed that provides robustness in many directions. It is demonstrated how to handle apparent outliers due to alternative distributional assumptions; and discriminate between outliers and large observations arising from non-linear responses. Two empirical applications, utilizing datasets popularized in previous applications, show substantive improvements from the proposed approach to robust model discovery.