Rates ofconvergence for minimal distances in the central limit theorem underprojective criteria

Jérôme Dedecker (Université Paris 6)
Florence Merlevède (Université Paris Est)
Emmanuel Rio (Université de Versailles)

Abstract


In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale differ- ence sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

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Pages: 978-1011

Publication Date: May 12, 2009

DOI: 10.1214/EJP.v14-648

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