  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.
