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Consistency of model selection and parameter estimation

Published online by Cambridge University Press:  14 July 2016

Ritei Shibata
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Abstract

The relationship between consistency of model selection and that of parameter estimation is investigated. It is shown that the consistency of model selection is achieved at the cost of a lower order of consistency of the resulting estimate of parameters in some domain. The situation is different when selecting autoregressive moving average models, since the information matrix becomes singular when overfitted. Some detailed analyses of the consistency are given in this case.

Keywords

AUTOREGRESSIVE PROCESSESAKAIKE INFORMATION CRITERIONFINITE PARAMETER ESTIMATION
Type
Part 2—Estimation for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 127 - 141
Copyright
Copyright © 1986 Applied Probability Trust 

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