SavedAdd your journal

Journals / International Econometric Review / 2010 / Cilt: 2 - Sayı: 2

Variance Estimates and Model Selection

Sıdıka BAŞÇI
Asad ZAMAN
Arzdar KİRACI
Pages
57–72
Publication Date
2010-09-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Such replacements improve the probability of finding the true model, at least in large samples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The large majority of the criteria for model selection are functions of the usual variance estimate for a regression model.
📊
Key Findings & Data:A cross validated variance estimate is more robust to specification errors (see, for example, Efron, 1983).
💡
Conclusion & Impact:Such replacements improve the probability of finding the true model, at least in large samples.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Autoregressive Process · Lag Order Determination · Model Selection Criteria

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.

🔖

Cite This Article

BAŞÇI, S., ZAMAN, A., KİRACI, A. (2010). Variance Estimates and Model Selection. International Econometric Review, Cilt: 2 - Sayı: 2, 57–72. https://ajindex.com/articles/832176

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. Akaike, H. (1973). Information Theory and an Extension of the Maximum Likelihood Principle. In 2nd International Symposium on Information Theory, ed. B.N. Petrov and F. Csàki. Budapest: Akadèmiai Kiadò, 267-281
  2. Akaike, H. (1974). A New Look at the Statistical Model IdentiŞcation. IEEE Transactions on Automatic Control, AC-19, 716-723.
  3. Allen, D.M. (1974). The Relationship Between Variable Selection and Data Augmentation and a Method for Prediction. Technometrics, 16, 125-7.
  4. Amemiya, T. (1980). Selection of Regressors. International Economic Review, 21, 331-345.
  5. Arlot, S. and A. Celisse (2010). A survey of cross-validation procedures for model selection. Statistics Surveys, 4, 40-79.
  6. Başçı, S. (1998). Computer Intensive Techniques for Model Selection. Ph. D. Dissertation, Bilkent University. Başçı, S. and A. Zaman (1998). Effects of Skewness and Kurtosis on Model Selection Criteria. Economics Letters, 59, 17-22.
  7. Başçı, S., M. Orhan, and A. Zaman (1998). Model Selection by Cross Validation: Computational Aspects. Working Paper, Bilkent University. Bhansali, R.J. and D.Y. Downham (1977). Some properties of the order of an autoregressive model selected by a generalized Akaike's EPF criterion. Biometrika, 64, 547-551.
  8. Billings, S.A., H.L. Wei (2008). An adaptive orthogonal search algorithm for model subset selection and non-linear system identification. International Journal of Control, 81(5), 714-724.
  9. Breiman, L. and D. Freedman (1983) How many variables should be entered in a regression equation? Journal of the American Statistical Association. 78, 131-136.
  10. Chatterjee, S. and A.S. Hadi (1988). Sensitivity Analysis in Linear Regression. John Wiley & Sons, Inc., New York. Christopher, T.B.S., A.M. Mokhtaruddin, M.H.A. Husni and M.Y. Abdullah (1998). A simple equation to determine the breakdown of individual aggregate size fractions in the wet- sieving method. Soil & Tillage Research, 45, 287-297
  11. Collett, D., K. Stepniewska (1999). Some practical issues in binary data analysis. Statistics in Medicine, 18(17-18), 2209-2221.
  12. Davies, S.L., A.A. Neath and J.E. Cavanaugh (2005). Cross validation model selection criteria for linear regression based on the Kullback-Leibler discrepancy. Statistical Methodology, 2(4), 249–266.
  13. Diebold, F.X. (1989). Forecast Combination and Encompassing: Reconciling Two Divergent Literatures. International Journal of Forecasting, 5(4), 589-92.
  14. Efron, B. (1983). Estimating the Error Rate of a Prediction Rule: Improvement on Cross- Validation