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- W1974862014 abstract "Let a density f on R d be estimated by f n(x, X 1, ..., X n) where x∈R d, f n is a Borel measurable function of its arguments, and X 1, ..., X n are independent random vectors with common density f. Let p≧1 be a constant. One of the main results of this note is that for every sequence f n, and for every positive number sequence a n satisfying lim a n=0, there exists an f such that $$Eleft( {smallint |f_n left( x right) - fleft( x right)|^p dx} right) > a_n$$ infinitely often. Here it suffices to look at all the f that are bounded by 2 and vanish outside [0, 1] d . For p=1, f can always be restricted to the class of infinitely many times continuously differentiable densities with all derivatives absolutely bounded and absolutely integrable." @default.
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- W1974862014 date "1983-01-01" @default.
- W1974862014 modified "2023-09-27" @default.
- W1974862014 title "On arbitrarily slow rates of global convergence in density estimation" @default.
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- W1974862014 doi "https://doi.org/10.1007/bf00534199" @default.
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