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The Distribution of the Stein-Rule Estimator in a Model with Non-Normal Disturbances

Published online by Cambridge University Press:  18 October 2010

John. L. Knight
John. L. Knight
Affiliation:
School of Economics, The University of New South Wales Department of Economics, University of Western Ontario
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Abstract

This paper derives the exact distribution and moments of the Stein-ruleestimator in a model where the disturbances follow a non-normal distribution of the Edgeworth or Gram-Charlier type. The results are achieved by combining the approach of Davis [4] for examining non-normality with the fractional calculus techniques of Phillips [11].

Type
Articles
Information
Econometric Theory , Volume 2 , Issue 2 , August 1986 , pp. 202 - 219
Copyright
Copyright © Cambridge University Press 1986

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References

1. Brandwein, A. C.Minimax Estimation of the Mean of Spherically Symmetric Distributions Under General Quadratic Loss. Journal of Multivariate Analysis (1979): 579–588.CrossRefGoogle Scholar
2. Brandwein, A. C. & Strawderman, W. E.. Minimax Estimation of Location Parameters for Spherically Symmetric Unimodal Distributions Under Quadratic Loss. Annals of Statistics (1978): 377–416.Google Scholar
3. Brandwein, A. C. & Strawderman, W. E.. Minimax Estimation of Location Parameters for Spherically Symmetric Distributions with Concave Loss. Annals of Statistics (1980): 279–284.Google Scholar
4. Davis, A. W.Statistical Distributions in Univariate and Multivariate Edgeworth Populations. Biometrika 63 (1976): 661–670.CrossRefGoogle Scholar
5. Gnanadesikan, R.Methods for Statistical Data Analysis of Multivariate Observations. New York: Wiley, 1977.Google Scholar
6. James, W. & and Stein, C.. Estimation with Quadratic Loss. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability pp. 361–379. Berkeley: University of California Press, 1961.Google Scholar
7. Knight, J. L.Non-normal Disturbances and the Distribution of the Durbin-Watson Statistic. Paper presented at the European Meeting of the Econometric Society, Pisa, September 1983.Google Scholar
8. Knight, J. L.Non-normal Errors and the Distribution of OLS and 2SLS Structural Estimators. Econometric Theory, 2 (1986): 75–106.CrossRefGoogle Scholar
9. Knight, J. L.The Moments of OLS and 2SLS When the Disturbances are Non-normal. Journal of Econometrics 27 (1985): 39–60.CrossRefGoogle Scholar
10. Knight, J. L.The Joint Characteristic Function of Linear and Quadratic Forms of Nonnormal Variables. Sankhya A 47 (1985): 231–238.Google Scholar
11. Phillips, P.C.B.The Exact Distribution of the Stein-rule Estimator. Journal of Econometrics 25 (1984): 123–131.CrossRefGoogle Scholar
12. Slater, L. J.Confluent Hyper geometric Functions. Cambridge: Cambridge University Press, 1960.Google Scholar
13. Srivastava, V. K. & Upadhyaya, S.. Properties of Stein-Like Estimators in Regression Models when Disturbances are Small. Journal of Statistical Research 11 (1977):5–21.Google Scholar
14. Ullah, A.On the Sampling Distribution of Improved Estimators for Coefficients in Linear Regression. Journal of Econometrics 2 (1974): 143–150.CrossRefGoogle Scholar
15. Ullah, A.The Exact, Large-Sample and Small-disturbance Conditions of Dominance of Biased Estimators in Linear Models. Economic Letters (1980): 339–344.CrossRefGoogle Scholar
16. Ullah, A.The Approximate Distribution of the Stein-rule Estimator. Economics Letters 10 (1982): 305–308.CrossRefGoogle Scholar
17. Ullah, A., Srivastava, V. K., & Chandra, R.. Properties of Shrinkage Estimators in Linear Regression When Disturbances are Not Normal. Journal of Econometrics 21 (1983): 389–402.CrossRefGoogle Scholar