Canadian Journal of Statistics

Estimation suroptimale de la densité par projection

Journal Article

Abstract

Superefficiency of a projection density estimator

The author constructs a projection density estimator with a data‐driven truncation index. This estimator reaches the superoptimal rates 1/n in mean integrated square error and {In ln(n/n}1/2 in uniform almost sure convergence over a given subspace which is dense in the class of all possible densities; the rate of the estimator is quasi‐optimal everywhere else. The subspace in question may be chosen a priori by the statistician.

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