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ORACLE EFFICIENT VARIABLE SELECTION IN RANDOM AND FIXED EFFECTS PANEL DATA MODELS

Published online by Cambridge University Press:  06 July 2012

Anders Bredahl Kock
Anders Bredahl Kock*
Affiliation:
Aarhus University and CREATES
*
*Address correspondence to: Anders Bredahl Kock, Department of Economics and Business, Aarhus University Fuglesangs Alle 4, 8210 Aarhus V, Denmark; e-mail:[email protected]
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Abstract

This paper generalizes the results for the Bridge estimator of Huang, Horowitz, and Ma (2008) to linear random and fixed effects panel data models which are allowed to grow in both dimensions. In particular, we show that the Bridge estimator isoracle efficient. It can correctly distinguish between relevant and irrelevant variables and the asymptotic distribution of the estimators of the coefficients of the relevant variables is the same as if only these had been included in the model, i.e. as if an oracle had revealed the true model prior to estimation.

In the case of more explanatory variables than observations we prove that the Marginal Bridge estimator can asymptotically correctly distinguish between relevant and irrelevant explanatory variables if the error terms are Gaussian. Furthermore, a partial orthogonality condition of the same type as in Huang et al. (2008) is needed to restrict the dependence between relevant and irrelevant variables.

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 1 , February 2013 , pp. 115 - 152
Copyright
Copyright © Cambridge University Press 2012 

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Footnotes

The author thanks Svend Erik Graversen, Niels Haldrup, Michael Jansson, Jørgen Hoffmann-Jørgensen, Adrian Pagan, Timo Teräsvirta, Allan Würtz, the co-editor, and an anonymous referee for help, comments, and suggestions. Also thanks to Joel Horowitz for responding quickly to my e-mails. All errors and shortcomings are my responsibility. Financial support from CREATES funded by the Danish National Research Foundation is gratefully acknowledged.

References

REFERENCES

Arellano, M. (2003) Panel Data Econometrics. Oxford University Press.CrossRefGoogle Scholar
Candes, E. & Tao, T. (2007) The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics 35, 2313–2351.CrossRefGoogle Scholar
Fan, J. & Lv, J. (2008) Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society, Series B 70, 849–911.CrossRefGoogle Scholar
Hoffmann-Jørgensen, J. (1994) Probability with a View Toward Statistics, vol. 1. Chapman & Hall/CRC.CrossRefGoogle Scholar
Huang, J., Horowitz, J., & Ma, S. (2008) Asymptotic properties of bridge estimators in sparse high-dimensional regression models. Annals of Statistics 36, 587–613.CrossRefGoogle Scholar
Hunter, D. & Li, R. (2005) Variable selection using MM algorithms. Annals of Statistics 33, 1617–1642.CrossRefGoogle ScholarPubMed
Knight, K. & Fu, W. (2000) Asymptotics for lasso-type estimators. Annals of Statistics 28, 1356–1378.Google Scholar
Meinshausen, N. & Yu, B. (2009) Lasso-type recovery of sparse representations for high-dimensional data. Annals of Statistics 37, 246–270.Google Scholar
Stoyanov, J. (1997) Counterexamples in Probability, 2nd ed. Wiley.Google Scholar
Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 73, 267–288.Google Scholar
Van der Vaart, A. & Wellner, J. (1996) Weak Convergence and Empirical Processes. Springer-Verlag.CrossRefGoogle Scholar
Zou, H. (2006) The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101, 1418–1429.CrossRefGoogle Scholar