Generalized quantile processes

J.H.J. Einmahl, D.M. Mason

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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.
Original languageEnglish
Pages (from-to)1062-1078
Number of pages17
JournalThe Annals of Statistics
Volume20
Issue number2
DOIs
Publication statusPublished - 1992

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Quantile Process
Functional Central Limit Theorem
Random Vector
Quantile
Univariate
Limiting

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Einmahl, J. H. J., & Mason, D. M. (1992). Generalized quantile processes. The Annals of Statistics, 20(2), 1062-1078. https://doi.org/10.1214/aos/1176348670
Einmahl, J.H.J. ; Mason, D.M. / Generalized quantile processes. In: The Annals of Statistics. 1992 ; Vol. 20, No. 2. pp. 1062-1078.
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Einmahl, JHJ & Mason, DM 1992, 'Generalized quantile processes', The Annals of Statistics, vol. 20, no. 2, pp. 1062-1078. https://doi.org/10.1214/aos/1176348670

Generalized quantile processes. / Einmahl, J.H.J.; Mason, D.M.

In: The Annals of Statistics, Vol. 20, No. 2, 1992, p. 1062-1078.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - 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.

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