Abstract
A nonparametric estimatef* of an unknown distribution densityf eW is called locally minimax iff it is minimax for all not too small neighborhoodsW g ,g eW∘, simultaneously, whereW∘ is some dense subset ofW. Radavicius and Rudzkis proved the existence of such an estimate under some general conditions. However, the construction of the estimate is rather complicated. In this paper, a new estimate is proposed. This estimate is locally minimax under some additional assumptions which usually hold for orthobases of algebraic polynomial and is almost as simple as the linear projective estimate. Thus, it takes a form convenient for the construction of an adaptive estimator, which does not usea-priori information about the smoothness of the density. The adaptive estimation problem is briefly discussed and an unknown density fitting by Jacobi polynomials is investigated more explicitly.
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