On quantiles and the central limit question for strongly mixing sequences
type: Item
instance of: scholarly article
title: On quantiles and the central limit question for strongly mixing sequences
zbMATH Open document ID: 0887.60028
DOI: 10.1023/A:1022624919588
published in: Journal of Theoretical Probability
publication date: 1998-05-25T00:00:00Z
review text: The author constructs three classes of strictly stationary strongly mixing random sequences in order to throw further light on the ``borderline'' of the central limit theorem for strictly stationary, strongly mixing random sequences. These examples involve the combining of ideas from the ``renewal type'' Markov chains that Davydov (1969, 1973) used as the basis for his counterexamples to the CLT, Barbee (1981), Herrndorf (1983) and Doukhan, Massart and Rio (1994). In particular in these constructions, a key role is played by quantiles in the central limit theorem under strong mixing -- a theme that was developed by Doukhan et al. (1994), on the basis of a covariance inequality proved by Rio (1993).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 1071665
zbMATH Keywords: strong mixing
zbMATH Keywords: central limit question
zbMATH Keywords: quantiles
author: Richard C. Bradley
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
full work available at URL: a:1022624919588
OpenAlex ID: W1537044570
description: scientific article; zbMATH DE number 1071665