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Distribution Theory of the Least Squares Averaging Estimator

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  • Liu, Chu-An

Abstract

This paper derives the limiting distributions of least squares averaging estimators for linear regression models in a local asymptotic framework. We show that the averaging estimators with fixed weights are asymptotically normal and then develop a plug-in averaging estimator that minimizes the sample analog of the asymptotic mean squared error. We investigate the focused information criterion (Claeskens and Hjort, 2003), the plug-in averaging estimator, the Mallows model averaging estimator (Hansen, 2007), and the jackknife model averaging estimator (Hansen and Racine, 2012). We find that the asymptotic distributions of averaging estimators with data-dependent weights are nonstandard and cannot be approximated by simulation. To address this issue, we propose a simple procedure to construct valid confidence intervals with improved coverage probability. Monte Carlo simulations show that the plug-in averaging estimator generally has smaller expected squared error than other existing model averaging methods, and the coverage probability of proposed confidence intervals achieves the nominal level. As an empirical illustration, the proposed methodology is applied to cross-country growth regressions.

Suggested Citation

  • Liu, Chu-An, 2013. "Distribution Theory of the Least Squares Averaging Estimator," MPRA Paper 54201, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:54201
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    Cited by:

    1. Gao, Yan & Zhang, Xinyu & Wang, Shouyang & Zou, Guohua, 2016. "Model averaging based on leave-subject-out cross-validation," Journal of Econometrics, Elsevier, vol. 192(1), pages 139-151.
    2. Tu, Yundong & Yi, Yanping, 2017. "Forecasting cointegrated nonstationary time series with time-varying variance," Journal of Econometrics, Elsevier, vol. 196(1), pages 83-98.
    3. Zhang, Xinyu, 2015. "Consistency of model averaging estimators," Economics Letters, Elsevier, vol. 130(C), pages 120-123.
    4. Aman Ullah & Xinyu Zhang, 2015. "Grouped Model Averaging for Finite Sample Size," Working Papers 201501, University of California at Riverside, Department of Economics.
    5. Giuseppe De Luca & Jan R. Magnus & Franco Peracchi, 2017. "Weighted-average least squares estimation of generalized linear models," EIEF Working Papers Series 1711, Einaudi Institute for Economics and Finance (EIEF), revised Aug 2017.
    6. Shangwei Zhao & Aman Ullah & Xinyu Zhang, 2018. "A Class of Model Averaging Estimators," Working Paper series 18-11, Rimini Centre for Economic Analysis.
    7. Steel, Mark F. J., 2017. "Model Averaging and its Use in Economics," MPRA Paper 81568, University Library of Munich, Germany.
    8. Zhang, Xinyu & Ullah, Aman & Zhao, Shangwei, 2016. "On the dominance of Mallows model averaging estimator over ordinary least squares estimator," Economics Letters, Elsevier, vol. 142(C), pages 69-73.
    9. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    10. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    11. repec:spr:metrik:v:80:y:2017:i:5:d:10.1007_s00184-017-0616-1 is not listed on IDEAS
    12. Naoya Sueishi & Arihiro Yoshimura, 2017. "Focused Information Criterion for Series Estimation in Partially Linear Models," The Japanese Economic Review, Japanese Economic Association, vol. 68(3), pages 352-363, September.
    13. Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    14. repec:eee:ecolet:v:162:y:2018:i:c:p:101-106 is not listed on IDEAS
    15. Shou-Yung Yin & Chu-An Liu & Chang-Ching Lin, 2016. "Focused Information Criterion and Model Averaging for Large Panels with a Multifactor Error Structure," IEAS Working Paper : academic research 16-A016, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    16. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.
    17. repec:eee:econom:v:204:y:2018:i:1:p:1-17 is not listed on IDEAS

    More about this item

    Keywords

    Local asymptotic theory; Model averaging; Model selection; Plug-in estimators.;

    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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