|
Histogram estimators of the shape of the concentration function in a two-component mixture
Author(s):
D.
I.
Pohyl'ko
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
125-133.
MSC (2000):
Primary 62G20;
Secondary 62G05
Posted:
September 5, 2006
Retrieve article in:
PDF DVI PostScript
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.
References:
-
- 1.
- R. E. Ma
 boroda, An asymptotically effective probability estimator constructed from observations of a mixture, Teor. Imovir. Mat. Stat. 59 (1998), 108-115; English transl. in Theory Probab. Math. Statist. 59 (1999), 121-128. MR 1793771 - 2.
- -, Nonparametric Statistics of Nonhomogeneous Observations, Doctoral dissertation, Kyiv, 1994. (Ukrainian)
- 3.
- -, Projection estimates for changing concentrations of mixtures, Teor. Imovir. Mat. Stat. 46 (1992), 70-76; English transl. in Theory Probab. Math. Statist. 46 (1993), 71-73. MR 1196209 (93j:62102)
- 4.
- -, An estimate of the distributions of the mixture components with varying concentrations, Ukrain. Mat. Zh. 48 (1996), no. 4, 562-566; English transl. in Ukrainian Math. J. 48 (1997), 618-622. MR 1417019 (97j:62055)
- 5.
- -, Statistical Analysis of Mixtures, Kyiv University, Kyiv, 2003. (Ukrainian)
- 6.
- C. K. Chui, Wavelets: A Mathematical Tool for Signal Processing, SIAM, Philadelphia, PA, 1997. MR 1443204 (99b:42012)
- 7.
- I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1996. MR 1162107 (93e:42045)
- 8.
- W. Härdle, Applied Nonparametric Regression, Cambridge University Press, Cambridge, 1990. MR 1161622 (93i:62030)
- 9.
- W. Härdle, G. Kerkyacharian, D. Picard, and A. Tsybakov, Wavelets, Approximation, and Statistical Applications, Springer-Verlag, New York, 1998. MR 1618204 (99f:42065)
- 10.
- R. E. Maiboroda, Estimation and classification by mixtures with time-dependent concentrations, VI International Vilnius Conference on Probability Theory and Math. Statistics. Abstracts of Communications, vol. 2, 1993, p. 48.
- 11.
- O. V. Sugakova, Asymptotics of a kernel estimate for distribution density constructed from observations of a mixture with varying concentration, Teor. Imovir. Mat. Stat. 59 (1999), 156-166; English transl. in Theory Probab. Math. Statist. 59 (2000), 161-171. MR 1793776
- 12.
- B. Vidakovic, Statistical Modeling by Wavelets, John Wiley & Sons, New York, 1999. MR 1681904 (2000f:42023)
Similar Articles:
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC
(2000):
62G20,
62G05
Retrieve articles in all Journals with MSC
(2000):
62G20,
62G05
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:
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):
26/MAY/2004
Posted:
September 5, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
|
Comments: webmaster@ams.org