Another proof of a slow convergence result of Birgé

Luc Devroye

Statistics & Probability Letters, 1995, vol. 23, issue 1, 63-67

Abstract: We give a short proof of the following result. Let fn be any density estimate based upon an i.i.d. sample drawn from a density f. For any monotone decreasing sequence {an} of positive numbers converging to zero with , a density f may be found such that for all n. This density may be picked from the class of densities on [0, 1] that are bounded by two. The proof of this fact simplifies an earlier proof by Birgé (1986) and extends a weaker lower bound by the author (1983).

Keywords: Density; estimation; Nonparametric; estimation; Lower; bounds; Minimax; theory; Rate; of; convergence (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (2)

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