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Variance Estimates and Model Selection

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  • Sidika Basci
  • Asad Zaman

Abstract

The large majority of the criteria for model selection are functions of the usual variance estimate for a regression model. The validity of the usual variance estimate depends on some assumptions, most critically the validity of the model being estimated. This is often violated in model selection contexts, where model search takes place over invalid models. A cross validated variance estimate is more robust to specification errors (see, for example, Efron, 1983). We consider the effects of replacing the usual variance estimate by a cross validated variance estimate, namely, the Prediction Sum of Squares (PRESS) in the functions of several model selection criteria. Such replacements improve the probability of finding the true model, at least in large samples.
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Suggested Citation

  • Sidika Basci & Asad Zaman, 1998. "Variance Estimates and Model Selection," Working Papers 9814, Department of Economics, Bilkent University.
    • Handle: RePEc:bil:wpaper:9814
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    References listed on IDEAS

    as
    1. Helmut Lütkepohl, 1985. "Comparison Of Criteria For Estimating The Order Of A Vector Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 35-52, January.
    2. Geweke, John & Meese, Richard, 1981. "Estimating regression models of finite but unknown order," Journal of Econometrics, Elsevier, vol. 16(1), pages 162-162, May.
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    4. Zaman, A., 1984. "Avoiding model selection by the use of shrinkage techniques," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 73-85.
    5. Magee, Lonnie & Veall, Michael R, 1991. "Selecting Regressors for Prediction Using PRESS and White t Statistics," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 91-96, January.
    6. McQuarrie, Allan & Shumway, Robert & Tsai, Chih-Ling, 1997. "The model selection criterion AICu," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 285-292, June.
    7. Amemiya, Takeshi, 1980. "Selection of Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 331-354, June.
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    2. Ozer Ozdemir & Memmedaga Memmedli & Akhlitdin Nizamitdinov, 2013. "ANN Models and Bayesian Spline Models for Analysis of Exchange Rates and Gold Price," International Econometric Review (IER), Econometric Research Association, vol. 5(2), pages 53-69, September.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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