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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Histogram estimators of the shape of the concentration function in a two-component mixture


Author: D. I. Pohyl'ko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 72 (2005).
Journal: Theor. Probability and Math. Statist. 72 (2006), 125-133
MSC (2000): Primary 62G20; Secondary 62G05
Published electronically: September 5, 2006
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct the projection estimators of the shape of the concentration function and obtain their expansions in the basis of indicator functions (the histogram basis) in the case where the data is a sample from a mixture of two components with unknown distributions whose concentrations are varying with observations. We prove that the estimators are consistent and find the rate of the almost sure convergence.


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Additional Information

D. I. Pohyl'ko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: pokhid@ukr.net

DOI: http://dx.doi.org/10.1090/S0094-9000-06-00670-3
PII: S 0094-9000(06)00670-3
Keywords: Projection estimates, estimates of the concentration, the shape of the concentration function
Received by editor(s): May 26, 2004
Published electronically: September 5, 2006
Article copyright: © Copyright 2006 American Mathematical Society