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Variance Estimates and Model Selection

  • Sýdýka Baþçý
  • Asad Zaman

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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Paper provided by Bilkent University, Department of Economics in its series Departmental Working Papers with number 9814.

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Date of creation: 1998
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Handle: RePEc:bil:bilpap:9814
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  1. Geweke, John F & Meese, Richard, 1981. "Estimating Regression Models of Finite but Unknown Order," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 55-70, February.
  2. 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.
  3. Francis X. Diebold, 1989. "Forecast combination and encompassing: reconciling two divergent literatures," Finance and Economics Discussion Series 80, Board of Governors of the Federal Reserve System (U.S.).
  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. 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 331-54, June.
  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. Baci, Sidika & Zaman, Asad, 1998. "Effects of skewness and kurtosis on model selection criteria," Economics Letters, Elsevier, vol. 59(1), pages 17-22, April.
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