Residual-based localization and quantification of peaks in X-ray diffractograms
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The Annals of Applied Statistics

Residual-based localization and quantification of peaks in X-ray diffractograms

P. L. Davies, U. Gather, M. Meise, D. Mergel, and T. Mildenberger

Source: Ann. Appl. Stat. Volume 2, Number 3 (2008), 861-886.

Abstract

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.

Keywords: Nonparametric regression; confidence regions; peak detection; x-ray diffractometry; thin film physics

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aoas/1223908044
Digital Object Identifier: doi:10.1214/08-AOAS181

References

Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 289–300.
Bernholt, T. and Hofmeister, T. (2006). An algorithm for a generalized maximum subsequence problem. In LATIN 2006: Theoretical Informatics (J. Correa, A. Hevia and M. Kiwi, eds.). Lecture Notes in Comput. Sci. 3887 178–189. Springer, Berlin.
Birkholz, M. (2006). Thin Film Analysis by X-Ray Scattering. Wiley-VCH, Weinheim.
Davies, P. and Kovac, A. (2001). Local extremes, runs, strings and multiresolution (with discussion). Ann. Statist. 29 1–65.
Davies, P. L. (1995). Data features. Statist. Neerlandica 49 185–245.
Davies, P. L. (2006). Long range financial data and model choice. Technical Report 21/06, Collaborative Research Centre 475, Dept. Statistics, Univ. Dortmund.
Davies, P. L., Kovac, A. and Meise, M. (2008). Nonparametric regression, confidence regions and regularization. Ann. Statist. To appear. arXiv:0711.0690 [math.ST].
Davies, P. L. and Meise, M. (2008). Approximating data with weighted smoothing splines. J. Nonparametr. Statist. 20 207–228.
Dümbgen, L. (2003). Optimal confidence bands for shape-restricted curves. Bernoulli 9 423–449.
Dümbgen, L. (2007). Confidence bands for convex median curves using sign-tests. In Asymptotics: Particles, Processes and Inverse Problems (E. Cator, G. Jongbloed, C. Kraaikamp, R. Lopuhaä and J. Wellner, eds.). IMS Lecture Notes—Monograph Series 55 85–100. IMS, Beachwood, OH.
Dümbgen, L. and Johns, R. (2004). Confidence bands for isotonic median curves using sign-tests. J. Comput. Graph. Statist. 13 519–533.
Dümbgen, L. and Spokoiny, V. (2001). Multiscale testing of qualitative hypotheses. Ann. Statist. 29 124–152.
Fletcher, R. (2000). Practical Methods of Optimization, 2nd ed. Wiley, Chichester.
Hall, Jr., M.M., Veeraraghavan, V. G., Rubin, H. and Winchell, P. G. (1977). The approximation of symmetric x-ray peaks by Pearson type vii distributions. J. Appl. Crystallography 10 66–68.
Johnson, N., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions. 2, 2nd ed. Wiley, New York.
Jupp, D. (1978). Approximation to data by splines with free knots. SIAM J. Numer. Anal. 15 328–343.
Kabluchko, Z. (2007). Extreme-value analysis of standardized Gaussian increments. arXiv:0706.1849v2 [math.PR].
Li, K.-C. (1989). Honest confidence regions for nonparametric regression. Ann. Statist. 17 1001–1008.
Mergel, D. (2006). Thin films of ITO as transparent elextrodes. Vakuum in Forschung und Praxis 18 15–18.
Mergel, D. and Qiao, Z. (2004). Correlation of lattice distortion with optical and electrical properties of In2O3:Sn films. J. Appl. Phys. 95 5608–5615.
Mergel, D., Stass, W., Ehl, G. and Barthel, D. (2000). Oxygen incorporation in thin films of In2O3:Sn prepared by radio frequency sputtering. J. Appl. Phys. 88 2437–2442.
Mergel, D., Thiele, T. and Qiao, Z. (2005). Texture analysis of thin In2O3:Sn films prepared by direct-current and radio-frequency magnetron-sputtering. J. Materials Research 20 2503–2509.
Mildenberger, T. (2008). A geometric interpretation of the multiresolution criterion in nonparametric regression. J. Nonparametr. Statist. 20 599–609.
Smart, L. and Moore, E. (2001). Solid State Chemistry—An Introduction. Nelson Thornes Ltd., Cheltenham, United Kingdom.

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