Pitman efficiencies of -goodness-of-fit tests
Why view and what is next?
N. N. Cencov wrote a commentary chapter included in the Appendix of the Russian translation of the Devroye and Györfi book [15] collecting some arguments supporting the view of density estimation. The Cencov’s work is available in Russian only and it hasn’t been translated, so late Igor Vajda decided to translate the Cencov’s paper and to add some remarks on the occasion of organizing the session “25 Years of the Density Estimation” at the Prague Stochastics 2010 Symposium. In this paper we...
Towards a universally consistent estimator of the Minkowski content
We deal with a subject in the interplay between nonparametric statistics and geometric measure theory. The measure () of the boundary of a set ⊂ ℝ (with ≥ 2) can be formally defined, a simple limit, by the so-called Minkowski content. We study the estimation of () from a sample of random points inside and outside . The sample design assumes that, for each sample point, we know (without error) whether or not that point belongs to . Under this design we suggest a...
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