Estimation of structure by minimum description length
This paper proves a theorem which shows that a previously derived minimum description length (MDL) estimation criterion can be used for distinguishing between structures in linear models for vector processes. This is done by considering an extreme case where the data are generated by a system falling outside of the linear space spanned by the coordinate system of the fitted models. The central result of the paper is the proof that in this case the inner product in the third term of the optimum description length: \[ -(1/N)\log P(y/\theta)+(k/2N)\log N+(k/2N)\log(\theta,I_{\theta}(y)\theta) \] grows to infinity with N, while it remains bounded if a model with the same structure as the data generating system is selected. The paper also presents a simple algorithm for estimating the best model, including its structure and the number of its parameters.
scientific article; zbMATH DE number 3860963