Informative Goodness-of-Fit for Multivariate Distributions

This article introduces an informative goodness-of-fit (iGOF) approach to study multivariate distributions. Conversely from standard goodness-of-fit tests, when the null model is rejected, iGOF allows us to identify the underlying sources of mismodelling and naturally equip practitioners with additional insights on the underlying data distribution. The informative character of the procedure proposed is achieved by introducing the \emph{joint comparison density}. As a result, the methods presented here naturally extend the seminal work of Parzen (1979) on univariate comparison distributions to the multivariate setting. Simulation studies show that iGOF enjoys high power for different types of alternatives.