On Asymptotic Properties of AIC Variants with Applications
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Abstract
In statistical modeling, the investigator is frequently confronted with the problem of selecting an appropriate model from a general class of candidate models. In recent years, various model selection procedures that can be used for the selection of the best possible model have been proposed. The AIC criterion [1] is considered the most popular tool for model selection although many competitors have been introduced over the years. One of the main drawbacks of AIC is its tendency to favor high dimensional models namely to overestimate the true model. A second issue that needs the attention of the investigator is the presence of outlying observations in the data set the inclusion of which in the statistical analysis may lead to erroneous results. In this work we propose AIC variants to handle the above weaknesses. Furthermore the asymptotic properties of the proposed criteria are investigated and a number of applications are discussed.
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