Geodesic
Adaptive estimation of distribution density
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 126-144 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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