Email this article Central Limit Theorem for a Wavelet Estimator of a Probability Density with a Given Weight
- Authors: Shestakov O.V.1,2
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Affiliations:
- Faculty of Computational Mathematics and Cybernetics
- Institute of Informatics Problems, Federal Research Center “Computer Science and Control”
- Issue: Vol 43, No 3 (2019)
- Pages: 143-147
- Section: Article
- URL: https://journals.rcsi.science/0278-6419/article/view/176269
- DOI: https://doi.org/10.3103/S0278641918040088
- ID: 176269
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Abstract
The problem of estimating a probability density with a given weight is considered. Probability densities of this type arise in different cases, e.g., analyzing order statistics and studying random-size samples in problems of reliability theory, insurance, and other areas. When constructing an estimator, expansion is used with respect to a wavelet basis based on wavelet functions with bounded spectrum. It is proved that the considered estimator is asymptotically normal when the number of terms of the expansion is fixed and growing.
About the authors
O. V. Shestakov
Faculty of Computational Mathematics and Cybernetics; Institute of Informatics Problems, Federal Research Center “Computer Science and Control”
Author for correspondence.
Email: oshestakov@cs.msu.su
Russian Federation, Moscow, 119991; Moscow, 119333
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