Adaptive estimating equations for a location parameter constructed by using observations with admixture
Authors:
R. Maĭboroda and O. Sugakova
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 80 (2010), 101-110
MSC (2000):
Primary 62G07; Secondary 62G20
DOI:
https://doi.org/10.1090/S0094-9000-2010-00797-6
Published electronically:
August 19, 2010
MathSciNet review:
2541955
Full-text PDF Free Access
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Additional Information
Abstract: A model of observations with admixture is considered. The distribution of the primary component of the model is symmetric and unknown, while the distribution of the admixture is known. Adaptive estimators are constructed for the median of the distribution of the primary component. The asymptotic variance of this estimator is close to the minimal asymptotic variance among all estimating equations estimators.
References
- O. Sugakova, Estimation of the mean from observations with an admixture, Teor. Ĭmovīr. Mat. Stat. 80 (2009), 128–137 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 80 (2010), 143–152. MR 2541959, DOI https://doi.org/10.1090/S0094-9000-2010-00801-5
- Anastasios A. Tsiatis, Semiparametric theory and missing data, Springer Series in Statistics, Springer, New York, 2006. MR 2233926
- Peter J. Bickel, Chris A. J. Klaassen, Ya’acov Ritov, and Jon A. Wellner, Efficient and adaptive estimation for semiparametric models, Johns Hopkins Series in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, MD, 1993. MR 1245941
- A. A. Borovkov, Matematicheskaya statistika, “Nauka”, Moscow, 1984 (Russian). Otsenka parametrov. Proverka gipotez. [Estimation of parameters. Testing of hypotheses]. MR 782295
- Laurent Bordes, Céline Delmas, and Pierre Vandekerkhove, Semiparametric estimation of a two-component mixture model where one component is known, Scand. J. Statist. 33 (2006), no. 4, 733–752. MR 2300913, DOI https://doi.org/10.1111/j.1467-9469.2006.00515.x
- Jun Shao, Mathematical statistics, 2nd ed., Springer Texts in Statistics, Springer-Verlag, New York, 2003. MR 2002723
References
- O. V. Sugakova, An estimator of the location parameter from observations with admixture, Teor. Imovirnost. Matem. Statyst. 80 (2009), 128–137; English transl. in this issue. MR 2541959 (2010e:62077)
- A. A. Tsiatis, Semiparametric Theory and Missing Data, Springer, Berlin, 2006. MR 2233926 (2007g:62009)
- P. Bickel, C. A. J. Klaassen, Ya. Ritov, and J. Wellner, Efficient and Adaptive Estimation for Semiparametric Models, J. Hopkins University Press, Baltimore–London, 1993. MR 1245941 (94m:62007)
- A. A. Borovkov, Mathematical Statistics, Nauka, Moscow, 1984; English transl., Gordon and Breach Science Publishers, Amsterdam, 1998. MR 782295 (86i:62001); MR 1712750 (2000f:62003)
- L. Bordes, C. Delmas, and P. Vandekerkhove, Semiparametric estimation of a two-component mixture model where one component is known, Scand. J. Statist. 33 (2006), 733–752. MR 2300913 (2008f:62049)
- J. Shao, Mathematical Statistics, Springer-Verlag, New York, 1998. MR 2002723 (2004g:62002)
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Additional Information
R. Maĭboroda
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
sugak@univ.kiev.ua
O. Sugakova
Affiliation:
Department of Higher Mathematics and Theoretical Radiophysics, Faculty for Radiophysics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
sugak@univ.kiev.ua
Keywords:
Method of moments,
a finite mixture of probability distributions,
consistence,
asymptotic normality,
coefficient of dispersion
Received by editor(s):
September 16, 2008
Published electronically:
August 19, 2010
Additional Notes:
Supported by the Swedish Institute grant SI-01424/2007.
Article copyright:
© Copyright 2010
American Mathematical Society
