City Research Online

Abstract

Given a finite number of data points, simulated from a mixture of exponentials, we propose two nonparametric techniques and a kernel method for estimating the mixing density function.

Firstly, an estimation technique based on Laplace transform, is introduced. We suggest a set of assumptions on which an estimation procedure is based. Simulations are presented that demonstrate the behaviour of the estimated mixing density. In this numerical study, some ways of improving the shape of the estimated density have been explored. Recommendations are given for controlling this shape.

A second estimation technique has been proposed by introducing a set of assumptions placing our estimation problem in an optimization form. The generalized simulated annealing algorithm (G.S.A) has been modified to adapt with our estimation setting. A criterion for measuring the performance of the adaptive (G.S.A.) is suggested. A sensitivity analysis of this adaptive algorithm is made, upon which some recommendations for improving its performance have been given.

In both of the above techniques a similarity is found between one of their parameters and the usual smoothing parameter in density estimation context. This is demonstrated by a numerical example in the case of the optimization technique.

A kernel method for estimating the mixing density is introduced within a Bayesian framework. Some characteristics (such as the limiting behaviour and the moment properties) of the derived kernel-type estimator, are studied. A graphical representation of the estimator, under two different values of (r), has been given using different sets of real data.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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