Generalized Quantile Processes
John H. J. Einmahl, David M. Mason
The Annals of Statistics · 1992 · Volume 20 · Issue 2
Abstract
For random vectors taking values in $\mathbb{R}^d$ we introduce a notion of multivariate quantiles defined in terms of a class of sets and study an associated process which we call the generalized quantile process. This process specializes to the well known univariate quantile process. We obtain functional central limit theorems for our generalized quantile process and show that both Gaussian and non-Gaussian limiting processes can arise. A number of interesting example are included.
Keywords
60F05; 62E20; 62G30; central limit theorem; empirical measure; generalized quantile; process;
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