Statistics – Applications
Scientific paper
2007-11-23
Annals of Applied Statistics 2008, Vol. 2, No. 3, 861-886
Statistics
Applications
Published in at http://dx.doi.org/10.1214/08-AOAS181 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins
Scientific paper
10.1214/08-AOAS181
We consider data consisting of photon counts of diffracted x-ray radiation as a function of the angle of diffraction. The problem is to determine the positions, powers and shapes of the relevant peaks. An additional difficulty is that the power of the peaks is to be measured from a baseline which itself must be identified. Most methods of de-noising data of this kind do not explicitly take into account the modality of the final estimate. The residual-based procedure we propose uses the so-called taut string method, which minimizes the number of peaks subject to a tube constraint on the integrated data. The baseline is identified by combining the result of the taut string with an estimate of the first derivative of the baseline obtained using a weighted smoothing spline. Finally, each individual peak is expressed as the finite sum of kernels chosen from a parametric family.
Davies Patrick Laurie
Gather Ursula
Meise M.
Mergel D.
Mildenberger Thoralf
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