Li, L. and Yu, B. (2000), `Iterated Logarithmic Expansions of the Pathwise Code Lengths for Exponential Families', IEEE Trans. on Information Theory, Vol. IT46, Nr. 7, November 2000. Home/Search Document Details and Download
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Strong Optimality of the Normalized ML Models as Universal Codes .. - Rissanen (2000) (8 citations) (Correct)
.... E f( Delta; fl) ln f(X n ; X n ) fl) f(X n ; fl) 1 Gamma ffl) k 2 ln n; which shows that ln C n (fl) 1. We chose not to assume the central limit theorem, because the assumptions made suffice; for instance, the second condition is shown to hold for exponential families in [7] without the assumption of the central limit theorem. Theorem 1 in the previous section dealt with the case where the data have regular features that are not captured by the models in the class M fl , and we found the NML density function among all density functions as ideal codes to minimize the ....
Li, L. and Yu, B. (2000), `Iterated Logarithmic Expansions of the Pathwise Code Lengths for Exponential Families', IEEE Trans. on Information Theory, Vol. IT46, Nr. 7, November 2000.
Strong Optimality of the Normalized ML Models as Universal Codes - Rissanen (2000) (8 citations) (Correct)
.... the maximum of the second term is (log e) e Gamma 1) we get the first claim (25) The exponential family satisfies all the five assumptions in [11] which imply that log C n is given by the formula for the stochastic complexity (9) and it grows to infinity with n; a different proof is given in [7]. If p and p are the infinum and the supremum, respectively, of p( over Omega Gamma we have by the assumption p=p K for some positive constant K. Since Z Omega p( d = C n pj Omega j pj Omega j=K; where jAj denotes the volume of a set A, we have jBj = Z B d ....
L. Li and B. Yu (1999), `Iterated Logarithmic Expansions of the Pathwise Code Lengths for Exponential Families', private communication.
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