Multivariate quantile-quantile plots and related tests using spatial quantiles (original) (raw)

The univariate quantile-quantile (Q-Q) plot is a well-known graphical tool for examining whether two data sets are generated from the same distribution or not. It is also used to determine how well a specified probability distribution fits a given sample. In this article, we consider an extension of Q-Q plot for multivariate data based on spatial quantiles introduced and studied by Chaudhuri (1996) and Koltchinskii (1997). The usefulness of the proposed graphical tool is illustrated on different real and simulated data some of which are fairly high dimensional. We also propose some statistical tests for distributions of multivariate samples based on spatial quantiles and study their performance compared to some other tests available in the existing literature.