Adaptive estimation of convex polytopes and convex sets from noisy data
نویسندگان
چکیده
منابع مشابه
Adaptive Estimation of Convex Sets and Convex Polytopes from Noisy Data
We estimate convex polytopes and general convex sets in R, d ≥ 2 in the regression framework. We measure the risk of our estimators using a L-type loss function and prove upper bounds on these risks. We show that, in the case of polytopes, these estimators achieve the minimax rate. For polytopes, this minimax rate is lnn n , which differs from the parametric rate for non-regular families by a l...
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2013
ISSN: 1935-7524
DOI: 10.1214/13-ejs804