Bernoulli

  • Bernoulli
  • Volume 11, Number 1 (2005), 131-189.

Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances

Eustasio Del Barrio, Evarist Giné, and Frederic Utzet

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Abstract

Weighted L2 functionals of the empirical quantile process appear as a component of many test statistics, in particular in tests of fit to location-scale families of distributions based on weighted Wasserstein distances. An essentially complete set of distributional limit theorems for the squared empirical quantile process integrated with respect to general weights is presented. The results rely on limit theorems for quadratic forms in exponential random variables, and the proofs use only simple asymptotic theory for probability distributions in Rn. The limit theorems are then applied to determine the asymptotic distribution of the test statistics on which weighted Wasserstein tests are based. In particular, this paper contains an elementary derivation of the limit distribution of the Shapiro-Wilk test statistic under normality.

Article information

Source
Bernoulli, Volume 11, Number 1 (2005), 131-189.

Dates
First available in Project Euclid: 7 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1110228245

Digital Object Identifier
doi:10.3150/bj/1110228245

Mathematical Reviews number (MathSciNet)
MR2121458

Zentralblatt MATH identifier
1063.62072

Keywords
distributional limit theorems tests of fit to location-scale families weighted L_2 norms of the quantile process weighted Wasserstein distance

Citation

Del Barrio, Eustasio; Giné, Evarist; Utzet, Frederic. Asymptotics for L 2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances. Bernoulli 11 (2005), no. 1, 131--189. doi:10.3150/bj/1110228245. https://projecteuclid.org/euclid.bj/1110228245


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