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August 2018 The function-indexed sequential empirical process under long-range dependence
Jannis Buchsteiner
Bernoulli 24(3): 2154-2175 (August 2018). DOI: 10.3150/17-BEJ924


Let $(\boldsymbol{X}_{j})_{j\geq1}$ be a multivariate long-range dependent Gaussian process. We study the asymptotic behavior of the corresponding sequential empirical process indexed by a class of functions. If some entropy condition is satisfied we have weak convergence to a linear combination of Hermite processes.


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Jannis Buchsteiner. "The function-indexed sequential empirical process under long-range dependence." Bernoulli 24 (3) 2154 - 2175, August 2018.


Received: 1 March 2016; Revised: 1 October 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839263
MathSciNet: MR3757526
Digital Object Identifier: 10.3150/17-BEJ924

Keywords: entropy condition , Hermite process , multivariate long-range dependence , sequential empirical process

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 3 • August 2018
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