JOURNAL OF THE JAPAN STATISTICAL SOCIETY
Online ISSN : 1348-6365
Print ISSN : 1882-2754
ISSN-L : 1348-6365
Articles
Bandwidth Selection in Deconvolution Kernel Distribution Estimators Defined by Stochastic Approximation Method with Laplace Errors
Yousri Slaoui
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2016 Volume 46 Issue 1 Pages 1-26

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Abstract

In this paper we consider the kernel estimators of a distribution function defined by the stochastic approximation algorithm when the observation are contamined by measurement errors. It is well known that this estimators depends heavily on the choice of a smoothing parameter called the bandwidth. We propose a specific second generation plug-in method of the deconvolution kernel distribution estimators defined by the stochastic approximation algorithm. We show that, using the proposed bandwidth selection and the stepsize which minimize the MISE (Mean Integrated Squared Error), the proposed estimator will be better than the classical one for small sample setting when the error variance is controlled by the noise to signal ratio. We corroborate these theoretical results through simulations and a real dataset.

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© 2016 Japan Statistical Society
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