Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Universal Residuals: A Multivariate Transformation

Publication Date

May, 2006

Publication Type

Tech Report


A. E. Brockwell


Rosenblatt's transformation has been used extensively for evaluation of model goodness-of-fit, but it only applies to models whose joint distribution is continuous. In this paper we generalize the transformation so that it applies to arbitrary probability models. The transformation is simple, but has a wide range of possible applications, providing a tool for exploratory data analysis and formal goodness-of-fit testing for a very general class of probability models. The method is demonstrated with specific examples.

(Revised 08/06)