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Regression model selection – a residual likelihood approach. (English) Zbl 1059.62074
Summary: We obtain the residual information criterion RIC, a selection criterion based on the residual log-likelihood, for regression models including classical regression models, Box-Cox transformation models, weighted regression models and regression models with autoregressive moving average errors. We show that RIC is a consistent criterion, and that simulation studies for each of the four models indicate that RIC provides better model order choices than the Akaike information criterion, corrected Akaike information criterion, final prediction error, $$C_p$$ and $$R^2_{\text{adj}}$$, except when the sample size is small and the signal-to-noise ratio is weak. In this case, none of the criteria performs well. Monte Carlo results also show that RIC is superior to the consistent Bayesian information criterion BIC when the signal-to-noise ratio is not weak, and it is comparable with BIC when the signal-to-noise ratio is weak and the sample size is large.

##### MSC:
 62J05 Linear regression; mixed models 62B10 Statistical aspects of information-theoretic topics 65C05 Monte Carlo methods
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