Robust statistics in Stata

Statistical methods often rely on restrictive assumptions that are expected to be (approximately) true in real life situations. For example, many classical statistical models ranging from descriptive statistics to regression models and/or multivariate analysis are based on the assertion that data are normally distributed. The main justification for assuming a normal distribution is that it generally approximates well many real life situations and, more conveniently, allows the derivation of explicit formulas for optimal statistical methods such as maximum likelihood estimators. However, the normality assumption may be violated in practice and results obtained via classical estimations may be uninformative or misleading. For example, it can happen that the vast majority of the observations are approximately normally distributed as assumed but a small cluster of so-called outliers is generated from a different distribution. In this situation, classical estimation techniques may break down and not convey the desired information. To deal with such limitations, robust statistical techniques have been developed. In this talk we will give a brief overview of situations in which robust methods should be used. We will start by describing "theoretically" such techniques in descriptive analysis, regression models, and multivariate statistics. We will then present some robust packages that have been implemented to make these estimators available (and fast to compute) in Stata. This talk is related to a forthcoming Stata Press book we are writing.