ON STOCHASTIC COMPLEXITY ESTIMATION - A DECISION-THEORETIC APPROACH

The concept of stochastic complexity developed by Rissanen leads to co nsistent probability density estimators. These density estimators are defined to achieve the best compromise between likelihood and simplici ty, namely, the stochastic complexity based on the observed sample. In this paper, a density estimation-based complexity decision rule is pr oposed which uses the quality of these estimators to estimate the corr esponding unknown element of the true probability density. In the deve lopment, we introduce a loss function which includes the total variati on of the squared distance of the characteristic functions to evaluate the performance of the density decision rule. The resulting complexit y density decision procedure is shown to be admissible, to achieve the minimum expected risk, and to form a minimal complete class.