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Data-driven Deconvolution Recursive Kernel Density Estimators Defined by Stochastic Approximation Method

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Abstract

In this paper we show how one can implement in practice the bandwidth selection in deconvolution recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm. We consider the so called super smooth case where the characteristic function of the known distribution decreases exponentially. We show that, using the proposed bandwidth selection and some special stepsizes, the proposed recursive estimator will be very competitive to the nonrecursive one in terms of estimation error and much better in terms of computational costs. We corroborate these theoretical results through simulations and a real dataset.

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Acknowledgements

I would like to thank the Editor and the referees for their very helpful comments, which led to a considerable improvement of the original version of the paper and a more sharply focused presentation.

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  1. Laboratoire de Mathématiques et Applications, Université de Poitiers, Chasseneuil, France

    Yousri Slaoui

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  1. Yousri Slaoui
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Slaoui, Y. Data-driven Deconvolution Recursive Kernel Density Estimators Defined by Stochastic Approximation Method. Sankhya A 83, 312–352 (2021). https://doi.org/10.1007/s13171-019-00182-3

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