## The Annals of Statistics

### Generalized Quantile Processes

#### 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.

#### Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 1062-1078.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348670

Digital Object Identifier
doi:10.1214/aos/1176348670

Mathematical Reviews number (MathSciNet)
MR1165606

Zentralblatt MATH identifier
0757.60012

JSTOR
links.jstor.org

#### Citation

Einmahl, John H. J.; Mason, David M. Generalized Quantile Processes. Ann. Statist. 20 (1992), no. 2, 1062--1078. doi:10.1214/aos/1176348670. https://projecteuclid.org/euclid.aos/1176348670