Title :
Asymptotic minimax regret for data compression, gambling and prediction
Author :
Xie, Qun ; Barron, Andrew R.
Author_Institution :
Dept. of Stat., Yale Univ., New Haven, CT, USA
fDate :
29 Jun-4 Jul 1997
Abstract :
The asymptotic minimax regret rn=minqmaxxn(log 1/q(xn)-log 1/p(xn|θˆ)) for the target family of memoryless sources on a given alphabet equals ((m-1)/2)logn+Cm+o(1). We determine the optimal constant Cm and we show that a slight modification of the Dirichlet (1/2, ..., 1/2) mixture is asymptotically minimax
Keywords :
data compression; encoding; game theory; minimax techniques; prediction theory; alphabet; asymptotic minimax regret; asymptotically minimax Dirichlet mixture; data compression; gambling; game theory; maximum likelihood estimator; memoryless sources; optimal constant; prediction; Data compression; Frequency; Indexing; Loss measurement; Maximum likelihood estimation; Minimax techniques; Statistics;
Conference_Titel :
Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on
Conference_Location :
Ulm
Print_ISBN :
0-7803-3956-8
DOI :
10.1109/ISIT.1997.613240
