Optimal third root asymptotic bounds in the statistical estimation of thresholds

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dc.creatorMerkl, Franz
dc.creatorMohammadi, Leila
dc.date2007-12-06
dc.date.accessioned2026-07-07T08:49:27Z
dc.date.available2026-07-07T08:49:27Z
dc.descriptionThis paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the estimation errors to be large on a scale determined by the inverse cube root of the sample size. As corollaries, we obtain probabilistic bounds for the prediction error in a classification problem. The key to the proof is an entropy estimate. The lower bounds are based on bounds for general estimators, which are applicable in other contexts as well. Furthermore, we introduce a class of optimal estimators whose errors asymptotically meet the border permitted by the lower bounds.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053607000000325 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0712.0894
dc.identifierhttp://arxiv.org/abs/0712.0894
dc.identifierAnnals of Statistics 2007, Vol. 35, No. 5, 2193-2218
dc.identifierdoi:10.1214/009053607000000325
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144303
dc.subjectStatistics Theory
dc.subject62G05 (Primary); 62G20 (Secondary)
dc.titleOptimal third root asymptotic bounds in the statistical estimation of thresholds
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