English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider the problem of model selection type aggregation in the context ofdensity estimation. We first show that empirical risk minimization issub-optimal for this problem and it shares this property with the exponentialweights aggregate, empirical risk minimization over the convex hull of thedictionary functions, and all selectors. Using a penalty inspired by recentworks on the $Q$-aggregation procedure, we derive a sharp oracle inequality indeviation under a simple boundedness assumption and we show that the rate isoptimal in a minimax sense. Unlike the procedures based on exponential weights,this estimator is fully adaptive under the uniform prior. In particular, itsconstruction does not rely on the sup-norm of the unknown density. By providinglower bounds with exponential tails, we show that the deviation term appearingin the sharp oracle inequalities cannot be improved.

Optimal exponential bounds for aggregation of density estimators