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An adaptive estimator of the density of components of a mixture
Author(s):
D.
I.
Pokhyl'ko
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 74
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 74
(2007),
147-162.
MSC (2000):
Primary 62G07;
Secondary 42C40
Posted:
July 5, 2007
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Additional information
Abstract:
Linear and nonlinear wavelet estimators of the density of components of a mixture are considered in the paper. The rate of convergence in the uniform metric and large deviation probabilities are obtained for linear estimators. The limit behavior of the threshold-based estimator is considered for the integral metric. An adaptive modification of the threshold-based estimator is constructed.
References:
-
- 1.
- L. Devroye and L. Gyorfi, Nonparametric Density Estimation. The
 View, John Wiley & Sons, Inc., New York, 1985. MR 780746 (86i:62065) - 2.
- Yu. V. Kozachenko, Lectures on the Theory of Wavelets, TBiMC, Kyiv, 2004. (Ukrainian)
- 3.
- R. E. Ma
 boroda, Estimation of distributions of the components of mixtures having varying concentrations, Ukr. Matem. Zh. 48 (1996), no. 4, 558-562; English transl. in Ukrainian Math. J. 48 (1997), no. 4, 618-622. MR 1417019 (97j:62055) - 4.
- R. E. Ma
 boroda, Statistical Analysis of Mixtures, ``Kyiv University'', Kyiv, 2003. (Ukrainian) - 5.
- D. I. Pokhyl'ko, Wavelet estimators of the density constructed from observations of mixture, Teor. Imovir. Mat. Stat. 70 (2004), 121-130; English transl. in Theory Probab. Math. Statist. 70 (2005), 135-145. MR 2109830 (2005i:62068)
- 6.
- 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 (1998), 156-166; English transl. in Theory Probab. Math. Statist. 59 (1999), 161-171. MR 1793776
- 7.
- I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1996. MR 1162107 (93e:42045)
- 8.
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- 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.
- B. Vidakovic, Statistical Modeling by Wavelets, John Wiley & Sons, New York, 1999. MR 1681904 (2000f:42023)
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(2000):
62G07,
42C40
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62G07,
42C40
Additional Information:
D.
I.
Pokhyl'ko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs'ka Street, 64, Kyiv 01033, Ukraine
Email:
pdi_2004@mail.ru
DOI:
10.1090/S0094-9000-07-00704-1
PII:
S 0094-9000(07)00704-1
Keywords:
Wavelets,
mixture,
estimator of the density,
adaptive estimator,
projective estimator
Received by editor(s):
27/JUN/2005
Posted:
July 5, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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