An Adaptive Estimation Procedure Using the LaPlace Transformation

Abstract

An adaptive parameter estimation procedure based upon the Laplace transformation is investigated. The parameter estimates are shown to be strongly consistent and asymptotically normally distributed when properly normalized. In the case that the parameters are the mixing parameters of a mixture of distributions, the parameter estimates are shown to be unbiased for any sample size. Computational experience and potential applications are included to demonstrate how this estimation procedure is especially useful to the reliability engineer.