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Model averaging estimator in ridge regression and its large sample properties

Author

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  • Shangwei Zhao

    (Minzu University of China)

  • Jun Liao

    (Capital Normal University)

  • Dalei Yu

    (Yunnan University of Finance and Economics)

Abstract

In linear regression, when the covariates are highly collinear, ridge regression has become the standard treatment. The choice of ridge parameter plays a central role in ridge regression. In this paper, instead of ending up with a single ridge parameter, we consider a model averaging method to combine multiple ridge estimators with $$M_n$$ M n different ridge parameters, where $$M_n$$ M n can go to infinity with sample size n. We show that when the fitting model is correctly specified, the resulting model averaging estimator is $$n^{1/2}$$ n 1 / 2 -consistent. When the fitting model is misspecified, the asymptotic optimality of the model averaging estimator is also established rigorously. The results of simulation studies and our case study concerning the urbanization level of Chinese ethnic areas demonstrate the usefulness of the model averaging method.

Suggested Citation

  • Shangwei Zhao & Jun Liao & Dalei Yu, 2020. "Model averaging estimator in ridge regression and its large sample properties," Statistical Papers, Springer, vol. 61(4), pages 1719-1739, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-018-1002-4
    DOI: 10.1007/s00362-018-1002-4
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    References listed on IDEAS

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