Opuscula Math. 39, no. 5 (2019), 733-746
https://doi.org/10.7494/OpMath.2019.39.5.733

 
Opuscula Mathematica

Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method

Yousri Slaoui

Abstract. In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a distribution function defined by the stochastic approximation algorithm. We show that the estimator constructed using the stepsize which minimize the Mean Integrated Squared Error (MISE) of the class of the recursive estimators defined by Mokkadem et al. gives the same pointwise large deviations principle (LDP) and moderate deviations principle (MDP) as the Nadaraya kernel distribution estimator.

Keywords: distribution estimation, stochastic approximation algorithm, large and moderate deviations principles.

Mathematics Subject Classification: 62G07, 62L20, 60F10.

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  • Yousri Slaoui
  • ORCID iD https://orcid.org/0000-0001-5295-3311
  • University of Poitiers, Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS, Téléport 2 - BP 30179, 11 Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France
  • Communicated by Andrzej Kozek.
  • Received: 2017-04-24.
  • Revised: 2019-01-29.
  • Accepted: 2019-03-30.
  • Published online: 2019-09-05.
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Cite this article as:
Yousri Slaoui, Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method, Opuscula Math. 39, no. 5 (2019), 733-746, https://doi.org/10.7494/OpMath.2019.39.5.733

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