Optimal third root asymptotic bounds in the statistical estimation of thresholds

Details Optimal third root asymptotic bounds in the statistical estimation of thresholds Optimal third root asymptotic bounds in the statistical estimation of thresholds

2007-12-06

arxiv.org/abs/0712.0894v1

Annals of Statistics 2007, Vol. 35, No. 5, 2193-2218

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000325 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000325

This 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.

Affiliated with

Also associated with

No associations

Rating

Optimal third root asymptotic bounds in the statistical estimation of thresholds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Optimal third root asymptotic bounds in the statistical estimation of thresholds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal third root asymptotic bounds in the statistical estimation of thresholds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-91633