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This article is cited in 4 scientific papers (total in 4 papers)
Adaptive estimation of distribution density
in the basis of algebraic polynomials
R. Rudzkis, M. Radavicius Institute of Mathematics and Informatics
Abstract:
This paper is devoted to the problem of adaptive statistical estimation
of the distribution density defined on a finite interval.
Projective-type estimators in the basis of Jacobi polynomials is
considered. An adaptive statistical estimator, which is asymptotically
minimax in the case of mean-square losses for all sets from a certain
family of contracting sets of functions having different smoothness, is constructed. The smoothness conditions are stated in terms of
$L_2$-norms of residuals of distribution densities when approximating them by linear combinations of
a finite number of the first Jacobi polynomials. Extension of the result to other orthonormal bases
possessing some natural regularity properties is also discussed.
Keywords:
adaptive estimation, locally minimax estimation, Jacobi polynomials, projective-type estimators, mean-square losses.
Received: 23.01.2001 Revised: 28.05.2003
Citation:
R. Rudzkis, M. Radavicius, “Adaptive estimation of distribution density
in the basis of algebraic polynomials”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 126–144; Theory Probab. Appl., 49:1 (2005), 93–109
Linking options:
https://www.mathnet.ru/eng/tvp239https://doi.org/10.4213/tvp239 https://www.mathnet.ru/eng/tvp/v49/i1/p126
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Abstract page: | 311 | Full-text PDF : | 165 | References: | 73 |
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