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Minimax Lower Bounds

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In estimation problems, lower bounds for the minimax risk are commonly used for assessing the quality of estimators. In this talk, a collection of such minimax lower bounds will be presented that involve a general class of dissimilarity measures between probabilities known as $f$-divergences. Connections to Kolmogorov’s notion of metric entropy will also be discussed. Further, two applications to nonparametric estimation problems involving shape restrictions will be presented.

This talk is part of the Statistics series.

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