Title :
Minimax lower bounds via f-divergences
Author :
Guntuboyina, Adityanand
Author_Institution :
Dept. of Stat., Yale Univ., New Haven, CT, USA
Abstract :
We prove a new lower bound for the minimax risk in estimation problems involving f-divergences between the underlying probability measures. The proof just uses the convexity of the function f and is extremely simple. Special cases and straightforward corollaries of our bound include well known inequalities for establishing minimax lower bounds such as Fano´s inequality, Pinsker´s inequality and inequalities based on global entropy conditions.
Keywords :
entropy; estimation theory; minimax techniques; probability; Fano inequality; Pinsker inequality; estimation problem; f-divergences; function convexity; global entropy condition; minimax lower bound; minimax risk; probability measures; Density measurement; Entropy; Extraterrestrial measurements; Minimax techniques; Probability; Q measurement; Statistics; Testing; Upper bound;
Conference_Titel :
Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on
Conference_Location :
Austin, TX
Print_ISBN :
978-1-4244-7890-3
Electronic_ISBN :
978-1-4244-7891-0
DOI :
10.1109/ISIT.2010.5513790
