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Moderate deviation principles for nonparametric recursive density estimators using Bernstein polynomials

Yousri Slaoui


In this paper, we prove moderate deviations principles for the recursive estimators of a density function defined by the stochastic approximation algorithm based on Bernstein polynomials introduced by Slaoui and Jmaei (2019). We showed that our considered estimator is more concentrated around the unknown density near of the edges compared to the standard nonparametric density estimators.


Bernstein polynomial; Density estimation; Large and Moderate deviations principles; Stochastic approximation algorithm.

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