Statistical and Information Theoretic Approaches to Model Selection and Averaging

TL;DRAbstract

In this thesis we consider model selection (MS) and its alternative, model averaging (MA), in seven research articles and in an introductory summary of the articles. The utilization of the minimum description length (MDL) principle is a common theme in five articles. In three articles we approach MA by estimating model weights using MDL and by making use of the idea of shrinkage estimation with special emphasis on the weighted average least squares (WALS) and penalized least squares (PenLS) estimation. We also apply MS and MA techniques to data on hip fracture treatment costs in seven hospital districts in Finland. \n\nImplementation of the MDL principle for MS is put into action by using the normalized maximum likelihood (NML). However, the straightforward use of the NML technique in Gaussian linear regression fails because the normalization coeffcient is not finite. Rissanen has proposed an elegant solution to the problem by constraining the data space properly. We demonstrate the ef

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