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Moderate deviation principles for nonparametric recursive distribution estimators using Bernstein polynomials

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In this paper we prove moderate deviations principles for the recursive estimators of a distribution function defined by the stochastic approximation algorithm based on Bernstein polynomials introduced by Jmaei el al. (J Nonparametr Stat 29:792–805, 2017). We show that the considered estimator gives the same pointwise moderate deviations principle (MDP) as the recursive kernel distribution estimator proposed in  Slaoui (Math Methods Stat 23(4):306–325, 2014b) and whose large and moderate deviation principles were established by  Slaoui (Stat Interface 12(3):439–455, 2009).

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The author would like to thank the Editor Editor-in-Chief Prof. Marco Castrillón López of Revista Matemática Complutense and the referees for their very helpful comments, which led to considerable improvement of the original version of the paper and a more sharply focused presentation.

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Correspondence to Yousri Slaoui.

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Slaoui, Y. Moderate deviation principles for nonparametric recursive distribution estimators using Bernstein polynomials. Rev Mat Complut 35, 147–158 (2022).

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