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Informational complexity criteria for regression models
This paper pursues three objectives in the context of multiple regression models: • • To give a rationale for model selection criteria which combine a badness-of-fit term (such as minus twice the maximum log likelihood) with a measure of complexity of model. We show that the ICOMP criter...
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Published in: | Computational statistics & data analysis 1998-07, Vol.28 (1), p.51-76 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | This paper pursues three objectives in the context of multiple regression models:
•
• To give a rationale for model selection criteria which combine a badness-of-fit term (such as minus twice the maximum log likelihood) with a measure of complexity of model. We show that the
ICOMP criterion introduced by Bozdogan can be seen as an approximation to the sum of two Kullback-Leibler distances, and that a criterion related to
ICOMP arises as an approximation to the posterior expectation of a certain utility.
•
• To investigate the asymptotic consistency properties of the class of
ICOMP criteria first in the case when one of the models considered is the true model and to introduce and establish a consistency property for the case when none of the models is the true model. In the first case, we find that asymptotic consistency holds under some assumptions; in this respect, some
ICOMP criteria resemble Akaike's
AIC, while other
ICOMP criteria resemble Schwarz's
BIC criterion. In the second case, in the context of regression models where at least one independent variable is missing in each model, we find that
ICOMP, as well as
AIC and
BIC are all asymptotically consistent.
•
• To investigate the finite sample behavior of
ICOMP criteria by means of a simulation study where none of the models considered is the true model. We find that the
ICOMP criteria tend to agree with decisions based on minimizing the Kullback-Leibler distance between the true model and each estimated model more often than
AIC or
BIC. This conclusion also holds when the true model is one of the models considered. |
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ISSN: | 0167-9473 1872-7352 |
DOI: | 10.1016/S0167-9473(98)00025-5 |