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James-Stein Type Estimator in Large Samples with Application to the Least Absolute Deviations Estimator

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  • Kim, Tae-Hwan
  • White, Halbert

Abstract

We explore the extension of James-Stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimator towards a fixed point, we shrink it towards a data-dependent point. We provide an analytic expression for the asymptotic risk and bias of James-Stein type estimators shrunk towards a data-dependent point and prove that they have smaller asymptotic risk than the base estimator. Shrinking an estimator toward a datadependent point turns out to be equivalent to combining two random variables using the James-Stein rule. We propose a general combination scheme which includes random combination (the James-Stein combination) and the usual nonrandom combination as special cases. As an example, we apply our method to combine the Least Absolute Deviations estimator and the Least Squares estimator. Our simulation study indicates that the resulting combination estimators have desirable finite sample properties when errors are drawn from symmetric distributions. Finally, using stock return data we present some empirical evidence that the combination estimators have the potential to improve out-of-sample prediction in terms of both mean square error and mean absolute error.

Suggested Citation

  • Kim, Tae-Hwan & White, Halbert, 2000. "James-Stein Type Estimator in Large Samples with Application to the Least Absolute Deviations Estimator," University of California at San Diego, Economics Working Paper Series qt3mn102zs, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt3mn102zs
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    References listed on IDEAS

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    1. Bates, Charles E. & White, Halbert, 1993. "Determination of Estimators with Minimum Asymptotic Covariance Matrices," Econometric Theory, Cambridge University Press, vol. 9(4), pages 633-648, August.
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    Cited by:

    1. Clarke, Judith A., 2008. "On weighted estimation in linear regression in the presence of parameter uncertainty," Economics Letters, Elsevier, vol. 100(1), pages 1-3, July.
    2. Peter Boatwright & Ajay Kalra & Wei Zhang, 2008. "Research Note--Should Consumers Use the Halo to Form Product Evaluations?," Management Science, INFORMS, vol. 54(1), pages 217-223, January.
    3. An, Lihua & Nkurunziza, Sévérien & Fung, Karen Y. & Krewski, Daniel & Luginaah, Isaac, 2009. "Shrinkage estimation in general linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2537-2549, May.
    4. Muhammad Qasim, 2024. "A weighted average limited information maximum likelihood estimator," Statistical Papers, Springer, vol. 65(5), pages 2641-2666, July.
    5. Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
    6. Tae-Hwan Kim, & Christophe Muller, 2012. "Bias Transmission and Variance Reduction in Two-Stage Quantile Regression," AMSE Working Papers 1221, Aix-Marseille School of Economics, France.
    7. Li, Haiqi & Chen, Xingyi & Liang, Jufang, 2022. "Shrinkage estimation of panel data models with interactive effects," Economics Letters, Elsevier, vol. 210(C).
    8. Judith Anne Clarke, 2017. "Model Averaging OLS and 2SLS: An Application of the WALS Procedure," Econometrics Working Papers 1701, Department of Economics, University of Victoria.
    9. Zou, Guohua & Wan, Alan T.K. & Wu, Xiaoyong & Chen, Ti, 2007. "Estimation of regression coefficients of interest when other regression coefficients are of no interest: The case of non-normal errors," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 803-810, April.

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