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作者：Strasser, H
摘要：In this paper we show that the well-known asymptotic efficiency bounds for full mixture models remain valid if individual sequences of nuisance parameters are considered. This is made precise both for some classes of random (i.i.d.) and nonrandom nuisance parameters. For the random case it is shown that superefficiency of the kind given by an example of Pfanzagl can happen only with low probability. The nonrandom case deals with permutation-invariant estimators under one-dimensional nuisance p...
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作者：Kerkyacharian, G; Picard, D
作者单位：Universite Paris Cite
摘要：Consider the problem of estimating integral Phi(f), where Phi is a smooth function and f is a density with given order of regularity s. Special attention is paid to the case Phi(t) = t(3). It has been shown that for low values of s the n (-1/2) late of convergence is not achievable uniformly over the class of objects of regularity s. In fact, a lower bound for this rate is n(-4s/(1+4s)) for 0 < s less than or equal to 1/4. AS for the upper bound, using a Taylor expansion, it can be seen that i...
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作者：Lugosi, G; Nobel, A
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We present general sufficient conditions for the almost sure L-1-consistency of histogram density estimates based on data-dependent partitions. Analogous conditions guarantee the almost-sure risk consistency of histogram classification schemes based on data-dependent partitions. Multivariate data are considered throughout. In each case, the desired consistency requires shrinking cells, subexponential growth of a combinatorial complexity measure and sublinear growth of the number of cells. It i...
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作者：Donoho, DL; Johnstone, IM; Kerkyacharian, G; Picard, D
作者单位：Universite de Picardie Jules Verne (UPJV); Universite Paris Cite
摘要：Density estimation is a commonly used test case for nonparametric estimation methods. We explore the asymptotic propel-ties of estimators based on thresholding of empirical wavelet coefficients. Minimax rates of convergence are studied over a large range of Besov function classes B-sigma pq and for a range of global L'(p) error measures, 1 less than or equal to p' less than or equal to infinity. A single wavelet threshold estimator is asymptotically minimax within logarithmic terms simultaneou...
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作者：Casalis, M; Letac, G
摘要：We characterize the Wishart distributions on a symmetric cone C. If C = (0, +infinity), this has been done by Lukacs in 1955. If C is the cone of positive definite symmetric matrices, this has been done by Olkin and Rubin in 1962. We both shorten and extend the Olkin-Rubin proof (sometimes obscure) by using three modern ideas: (i) try to avoid artificial coordinates in differential geometry; (ii) the variance function of a natural exponential family F characterizes F; (iii) symmetric matrices ...
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作者：Anderson, TW
摘要：Under appropriate conditions the probability of a convex symmetric set decreases as the spread or scatter of the distribution increases. This paper studies the conditions when the random vector has a symmetric unimodal distribution.
