Adaptive estimation of distribution density
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 126-144
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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.
@article{TVP_2004_49_1_a6,
author = {R. Rudzkis and M. Radavicius},
title = {Adaptive estimation of distribution density},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {126--144},
publisher = {mathdoc},
volume = {49},
number = {1},
year = {2004},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a6/}
}
R. Rudzkis; M. Radavicius. Adaptive estimation of distribution density. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 126-144. http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a6/