Minimum description length estimators under the optimal coding scheme

Abstract

Following Rissanen we consider the statistical model {Pø} as a code-book, ø indexing the codes. To obtain a single code, we first encode some ø and then encode our data x with the code corresponding to this ø. Rissanen's minimum description length principle recommends using the value of ø minimizing the total code length as an estimate of ø given the data a:. For some standard statistical models we find easily computable estimators which respect this principle when ø is encoded with the asymptotically optimal coding scheme due to Levin and Chaitin.