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Least squares model averaging by Mallows criterion

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  • Wan, Alan T.K.
  • Zhang, Xinyu
  • Zou, Guohua

Abstract

This paper is in response to a recent paper by Hansen (2007) who proposed an optimal model average estimator with weights selected by minimizing a Mallows criterion. The main contribution of Hansen's paper is a demonstration that the Mallows criterion is asymptotically equivalent to the squared error, so the model average estimator that minimizes the Mallows criterion also minimizes the squared error in large samples. We are concerned with two assumptions that accompany Hansen's approach. The first is the assumption that the approximating models are strictly nested in a way that depends on the ordering of regressors. Often there is no clear basis for the ordering and the approach does not permit non-nested models which are more realistic from a practical viewpoint. Second, for the optimality result to hold the model weights are required to lie within a special discrete set. In fact, Hansen noted both difficulties and called for extensions of the proof techniques. We provide an alternative proof which shows that the result on the optimality of the Mallows criterion in fact holds for continuous model weights and under a non-nested set-up that allows any linear combination of regressors in the approximating models that make up the model average estimator. These results provide a stronger theoretical basis for the use of the Mallows criterion in model averaging by strengthening existing findings.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 156 (2010)
Issue (Month): 2 (June)
Pages: 277-283

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Handle: RePEc:eee:econom:v:156:y:2010:i:2:p:277-283

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Asymptotic optimality Continuous weights Mallows criterion Non-nested models;

References

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  1. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Can One Estimate the Unconditional Distribution of Post-Model-Selection Estimators ?," MPRA Paper 72, University Library of Munich, Germany.
  2. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
  3. Yuan, Zheng & Yang, Yuhong, 2005. "Combining Linear Regression Models: When and How?," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1202-1214, December.
  4. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
  5. Hannes Leeb & Benedikt M. Poetscher, 2000. "The Finite-Sample Distribution of Post-Model-Selection Estimators, and Uniform Versus Non-Uniform Approximations," Econometrics 0004001, EconWPA.
  6. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
  7. Kabaila, Paul, 2002. "On Variable Selection In Linear Regression," Econometric Theory, Cambridge University Press, vol. 18(04), pages 913-925, August.
  8. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  9. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
  10. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
  11. Pötscher, Benedikt M., 2006. "The Distribution of Model Averaging Estimators and an Impossibility Result Regarding Its Estimation," MPRA Paper 73, University Library of Munich, Germany, revised Jul 2006.
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Citations

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Cited by:
  1. Liu, Qingfeng, 2010. "Generalized Cp Model Averaging for Heteroskedastic Models," ビジネス創造センターディスカッション・ペーパー (Discussion papers of the Center for Business Creation) 10252/4334, Otaru University of Commerce.
  2. Zhang, Xinyu & Lu, Zudi & Zou, Guohua, 2013. "Adaptively combined forecasting for discrete response time series," Journal of Econometrics, Elsevier, vol. 176(1), pages 80-91.
  3. Tian Xie, 2012. "Least Squares Model Averaging by Prediction Criterion," Working Papers 1299, Queen's University, Department of Economics.
  4. Zhang, Xinyu & Wan, Alan T.K. & Zou, Guohua, 2013. "Model averaging by jackknife criterion in models with dependent data," Journal of Econometrics, Elsevier, vol. 174(2), pages 82-94.
  5. Aman Ullah & Huansha Wang, 2013. "Parametric and Nonparametric Frequentist Model Selection and Model Averaging," Econometrics, MDPI, Open Access Journal, vol. 1(2), pages 157-179, September.
  6. Toru Kitagawa & Chris Muris, 2013. "Covariate selection and model averaging in semiparametric estimation of treatment effects," CeMMAP working papers CWP61/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
  8. Magnus, Jan R. & Wan, Alan T.K. & Zhang, Xinyu, 2011. "Weighted average least squares estimation with nonspherical disturbances and an application to the Hong Kong housing market," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1331-1341, March.
  9. Magnus, J.R. & Wang, W. & Zhang, Xinyu, 2012. "WALS Prediction," Discussion Paper 2012-043, Tilburg University, Center for Economic Research.
  10. Schomaker, Michael & Heumann, Christian, 2014. "Model selection and model averaging after multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 758-770.
  11. Zhang, Xinyu, 2013. "Model averaging with covariates that are missing completely at random," Economics Letters, Elsevier, vol. 121(3), pages 360-363.
  12. Michael Schomaker, 2012. "Shrinkage averaging estimation," Statistical Papers, Springer, vol. 53(4), pages 1015-1034, November.
  13. Wan, Alan T.K. & Zhang, Xinyu & Wang, Shouyang, 2014. "Frequentist model averaging for multinomial and ordered logit models," International Journal of Forecasting, Elsevier, vol. 30(1), pages 118-128.
  14. Liu, Chu-An, 2012. "A plug-in averaging estimator for regressions with heteroskedastic errors," MPRA Paper 41414, University Library of Munich, Germany.

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