Bandwidth selection in deconvolution kernel distribution estimators defined by stochastic approximation method with Laplace errors

TL;DR

This paper introduces a new bandwidth selection method for deconvolution kernel distribution estimators using stochastic approximation, improving estimation accuracy in small samples with Laplace errors.

Contribution

It proposes a second-generation plug-in bandwidth selection method tailored for stochastic approximation-based deconvolution estimators with Laplace errors.

Findings

Proposed method outperforms classical estimators in small samples.

Theoretical results are supported by simulations and real data.

Optimal stepsize minimizes MISE for better estimation.

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.