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On the sparsity of Mallows model averaging estimator

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  • Feng, Yang
  • Liu, Qingfeng
  • Okui, Ryo

Abstract

We show that Mallows model averaging estimator proposed by Hansen (2007) can be written as a least squares estimation with a weighted L1 penalty and additional constraints. By exploiting this representation, we demonstrate that the weight vector obtained by this model averaging procedure has a sparsity property in the sense that a subset of models receives exactly zero weights. Moreover, this representation allows us to adapt algorithms developed to efficiently solve minimization problems with many parameters and weighted L1 penalty. In particular, we develop a new coordinate-wise descent algorithm for model averaging. Simulation studies show that the new algorithm computes the model averaging estimator much faster and requires less memory than conventional methods when there are many models.

Suggested Citation

  • Feng, Yang & Liu, Qingfeng & Okui, Ryo, 2020. "On the sparsity of Mallows model averaging estimator," Economics Letters, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:ecolet:v:187:y:2020:i:c:s0165176519304653
    DOI: 10.1016/j.econlet.2019.108916
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    References listed on IDEAS

    as
    1. Zhang, Xinyu & Liu, Chu-An, 2019. "Inference After Model Averaging In Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 35(4), pages 816-841, August.
    2. Qingfeng Liu & Ryo Okui, 2013. "Heteroscedasticity‐robust C(p) model averaging," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 463-472, October.
    3. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, December.
    4. Enrique Moral-Benito, 2015. "Model Averaging In Economics: An Overview," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 46-75, February.
    5. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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    Citations

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    Cited by:

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    3. Tianming Gao & Vasilii Erokhin, 2020. "Capturing a Complexity of Nutritional, Environmental, and Economic Impacts on Selected Health Parameters in the Russian High North," Sustainability, MDPI, vol. 12(5), pages 1-25, March.
    4. Yang Feng & Qingfeng Liu, 2020. "Nested Model Averaging on Solution Path for High-dimensional Linear Regression," Papers 2005.08057, arXiv.org.
    5. Vasilii Erokhin & Li Diao & Tianming Gao & Jean-Vasile Andrei & Anna Ivolga & Yuhang Zong, 2021. "The Supply of Calories, Proteins, and Fats in Low-Income Countries: A Four-Decade Retrospective Study," IJERPH, MDPI, vol. 18(14), pages 1-30, July.

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    More about this item

    Keywords

    Sparsity; Model averaging; L1 penalty; Coordinate-wise descent algorithm;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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