B-Spline deconvolution based on the Em algorithm

Abstract

B-splines are considered for the decon volution problem of estimating a probability density function when the sample observations are contaminated with random noise. In the logspline method of density estimation, the logarithm of the unknown density function is approximated by a polynomial spline, the unknown parameters of which are estimated by maximum likelihood. Based on the logspline method, a fully automated procedure involving the EM algorithm, stepwise knot deletion and BIC has been developed for decon volution. Numerical examples using simulated data are given to show the performance of the B-spline deconvolution.

Keywords:

• Deconvolution
• B-splines
• EM algorithm
• stepwise knot deletion
• model selection