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Moderate deviation principles for nonparametric recursive distribution estimators using Bernstein polynomials
Revista Matemática Complutense ( IF 1.4 ) Pub Date : 2021-01-12 , DOI: 10.1007/s13163-021-00384-0
Yousri Slaoui

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).



中文翻译:

使用伯恩斯坦多项式的非参数递归分布估计量的中偏差原理

在本文中,我们证明了由Jmaei等人介绍的基于伯恩斯坦多项式的随机逼近算法定义的分布函数的递归估计量的适度偏差原理。(J Nonparametr Stat 29:792–805,2017)。我们证明,所考虑的估算器给出了与Slaoui中提出的递归核分布估算器相同的逐点中等偏差原理(MDP)(Math Methods Stat 23(4):306-325,2014b),其大和中等偏差原理由Slaoui(Stat Interface 12(3):439-455,2009)。

更新日期:2021-01-12
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