Deconvolution of Microfluorometric Histograms withBSplines

Abstract

We consider the problem of estimating a probability density from observations from that density which are further contaminated by random errors. We propose a method of estimation using spline functions, discuss the numerical implementation of the method, and prove its consistency. The problem is motivated by the analysis of DNA content obtained by microfluorometry , and an example of such an analysis is included.

Deconvolving a density from contaminated dependent observations

“…A variety of approaches for estimation of g have been considered in the literature: a maximunl likelihood method is given in Snyder et al (1988), B-Splines are used by Mendelsohn and Rice (1982), and in Masry and Rice (1992) Gaussian deconvolution is based on estimates of derivatives of g. Liu and Taylor (1989) seems to be the first published work that investigates the performance of kerneltype estimators in this context. Other work on deconvolving kernel estimators includes Zhang (1990), Stefanski (1990), Fan et al (1990), Stefanski and Carroll (1990), Fan (1991aFan ( , 1991bFan ( , 1992, Fan and Truong (1993), Fan and Masry (1992), and Masry (1991aMasry ( , 1991bMasry ( , 1993aMasry ( , 1993b.…”

“…(1984). Further applications are mentioned in Carroll and Hall (1988) and Zhang (1990), Crmnp and Seinfeld (1982), Mendelsohn and Rice (1982), Snyder et al (1988) and some of the references therein.…”

Analysis of time-of-flight data constraints and error bars

“…A similar approach has been used in the deconvolution of microfluorimetric data from DNA analysis [3] and a good illustration of the use of spline functions in data analysis is provided by Wold [4]. An energy interval [Emin, Emax] is split into a series of sections defined by a series of knot points {k0, kl,... ,kN} which can be equally spaced or can be chosen by another criterion.…”

“…Expressing p(E) as a sum over the B-spline basis means that the effect of T on the B-splines must be evaluated, equation (3). Once the set of knot points has been chosen, the B-splines are defined and they can then be transformed.…”