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

Author:
D. I. Pohyl’ko

Translated by:
S. Kvasko

Journal:
Theor. Probability and Math. Statist. **72** (2006), 125-133

MSC (2000):
Primary 62G20; Secondary 62G05

DOI:
https://doi.org/10.1090/S0094-9000-06-00670-3

Published electronically:
September 5, 2006

MathSciNet review:
2168142

Full-text PDF Free Access

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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

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