×

Kernel estimation in high-energy physics. (English) Zbl 0973.81546

Summary: Kernel estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of kernel estimation is developed for univariate and multivariate settings. The second section discusses some of the applications of kernel estimation to high-energy physics. The third section provides an overview of the available univariate and multivariate packages. This paper concludes with a discussion of the inherent advantages of kernel estimation techniques and systematic errors associated with the estimation of parent distributions.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81-04 Software, source code, etc. for problems pertaining to quantum theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Scott, D., Multivariate Density Estimation: Theory, Practice, and Visualization (1992), John Wiley and Sons Inc: John Wiley and Sons Inc New York · Zbl 0850.62006
[2] Abramson, I., On bandwidth variation in kernel estimates: a square root law, Ann. Statist., 10, 1217-1223 (1982) · Zbl 0507.62040
[3] Cranmer, K., Kernel estimation for parametrization of discriminant variable distributions, ALEPH 99-144 PHYSICS 99-056 (1999)
[4] Search for neutral Higgs bosons in \(e^+e^−\) collisions at \(s≈ 192-202\) GeV, OPAL Physics Note PN426 (2000)
[5] Hu, H.; Nielsen, J., Analytic confidence level calculations using the likelihood ratio and fourier transform, (James, F.; Lyons, L.; Perrin, Y., Workshop on Confidence Limits, CERN 2000-005 (2000)), 109
[6] The \(Ba B B\); The \(Ba B B\)
[7] Knuteson, B.; Miettinen, H.; Holmström, L., Mass analysis and parameter estimation with PDE, D∅ Note 003396 (1998)
[8] Holmström, L.; Miettinen, H.; Sain, S. R., A new multivariate technique for top quark search, Comput. Phys. Comm., 88, 195-210 (1995)
[9] Miettinen, H.; Epply, G., Possible hint of top → \(e^+E̷t+\) jets, D∅ Note 002145 (1994)
[10] Miettinen, H., Top quark results from D∅, D∅ Note 002527 (1995)
[11] Frodesen, A.; Skjeggestad, O., Probab. Statist. Particle Phys., 424-427 (1979)
[12] Allison, J., Multiquadric radial basis functions for representing multidimensional high energy physics data, Comput. Phys. Comm., 77, 377-395 (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.