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Theory of Probability and Mathematical Statistics

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Order of approximation in the central limit theorem for associated random variables and a moderate deviation result


Author: M. Sreehari
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 229-242
MSC (2010): Primary 60E15, 60F10
DOI: https://doi.org/10.1090/tpms/1073
Published electronically: August 19, 2019
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Abstract: An estimate of the order of approximation in the central limit theorem for strictly stationary associated random variables with finite moments of order $ q > 2$ is obtained. A moderate deviation result is also obtained. We have a refinement of recent results in Çagin et al.,J.Korean Statist.Soc.45 (216), no. 2, 285-294. The order of approximation obtained here is an improvement over the corresponding result of Wood in Ann. Probab. 11 (1983), no. 4, 1042-1047.


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Additional Information

M. Sreehari
Affiliation: Department of Statistics, The M. S. University of Baroda, Vadodara, 390002, India
Address at time of publication: 6-B, Vrundavan Park, New Sama Road, Vadodara 390024, India
Email: msreehari03@yahoo.co.uk

DOI: https://doi.org/10.1090/tpms/1073
Keywords: Associated random variables, central limit theorem, rate of convergence, Berry--Ess\'een type bound, moderate deviations
Received by editor(s): November 14, 2017
Published electronically: August 19, 2019
Article copyright: © Copyright 2019 American Mathematical Society