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James-Stein Type Estimators 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 data-dependent 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.

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Bibliographic Info

Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt4zq9k3qh.

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Date of creation: 01 May 2000
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Handle: RePEc:cdl:ucsdec:qt4zq9k3qh

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Keywords: shrinkage; asymptotic risk; combination estimator;

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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(04), pages 633-648, August.
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Cited by:
  1. 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, Marseille, France.
  2. Judge, George G. & Mittelhammer, Ronald C, 2003. "A semi-parametric basis for combining estimation problems under quadratic loss," CUDARE Working Paper Series 948, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  3. 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.
  4. Judith A. Clarke, 2007. "On Weighted Estimation in Linear Regression in th Presence of Parameter Uncertainty," Econometrics Working Papers 0701, Department of Economics, University of Victoria.

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