Abstract :
In this paper a connection between the problems of prediction, data compression, and statistical estimation is established with the central notion being the information in a string relative to a class of processes. The earlier derived MDL-criterion for estimation of parameters, including their number, is given a fundamental information theoretic justification by showing that its estimators achieve the information in the strings. It is also shown that one cannot do prediction in gaussian ARMA processes below a bound, which is completely determined by the same estimators.
