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Lower bounds on expected redundancy for nonparametric classes

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1 Author(s)
Bin Yu ; Dept. of Stat., California Univ., Berkeley, CA, USA

The article focuses on lower bound results on expected redundancy for universal coding of independent and identically distributed data on [0, 1] from parametric and nonparametric families. After reviewing existing lower bounds, we provide a new proof for minimax lower bounds on expected redundancy over nonparametric density classes. This new proof is based on the calculation of a mutual information quantity, or it utilizes the relationship between redundancy and Shannon capacity. It therefore unifies the minimax redundancy lower bound proofs in the parametric and nonparametric cases

Published in:

IEEE Transactions on Information Theory  (Volume:42 ,  Issue: 1 )