Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal exponential bounds for aggregation of density estimators   We consider the problem of model selection type aggregation in the context of
density estimation. We first show that empirical risk minimization is
sub-optimal for this problem and it shares this property with the exponential
weights aggregate, empirical risk minimization over the convex hull of the
dictionary functions, and all selectors. Using a penalty inspired by recent
works on the $Q$-aggregation procedure, we derive a sharp oracle inequality in
deviation under a simple boundedness assumption and we show that the rate is
optimal in a minimax sense. Unlike the procedures based on exponential weights,
this estimator is fully adaptive under the uniform prior. In particular, its
construction does not rely on the sup-norm of the unknown density. By providing
lower bounds with exponential tails, we show that the deviation term appearing
in the sharp oracle inequalities cannot be improved.

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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio