Adaptive nonparametric confidence sets
نویسندگان
چکیده
منابع مشابه
Adaptive Nonparametric Confidence Sets
We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the dia...
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We present a method for constructing nonparametric confidence sets for density functions based on an approach due to Beran and Dümbgen (1998). We expand the density in an appropriate basis and we estimate the basis coefficients by using linear shrinkage methods. We then find the limiting distribution of an asymptotic pivot based on the quadratic loss function. Inverting this pivot yields a conf...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2006
ISSN: 0090-5364
DOI: 10.1214/009053605000000877