Title :
Asymptotically optimum selections in convex families
Author_Institution :
Inf. Syst. Lab., Stanford Univ., CA, USA
fDate :
29 Jun-4 Jul 1997
Abstract :
Let χ be a standard Borel space and for r⩽s and let Xrs=(Xr,...Xs). For n⩾1 let Xn=(X0,...Xn-1) and let 𝒬n be a convex family of measurable functions q(xn )⩾0 on χn. A function q*(xn) is log-optimum in 𝒬n under a probability distribution P on χn if it attains W(𝒬n)(P(Xn))=sup(q(xn) in Qn )EP{log q(Xn)}. The author provides a universal scheme for making selections in a multiplicative sequence of convex model classes, where the duality between maximizing growth exponents and minimizing information rates is obvious
Keywords :
channel capacity; probability; sequences; statistical analysis; asymptotically optimum selections; convex families; convex model classes; growth exponents; information rates; measurable functions; multiplicative sequence; probability distribution; standard Borel space; Bellows; Convergence; Information rates; Information systems; Portfolios; Probability distribution; Q measurement; Random variables; Time measurement;
Conference_Titel :
Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on
Conference_Location :
Ulm
Print_ISBN :
0-7803-3956-8
DOI :
10.1109/ISIT.1997.613199
