Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-01T21:11:30.703Z Has data issue: false hasContentIssue false

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
Affiliation:
School of Economics, The University of New South Wales Department of Economics, University of Western Ontario

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
Copyright
Copyright © Cambridge University Press 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Brandwein, A. C.Minimax Estimation of the Mean of Spherically Symmetric Distributions Under General Quadratic Loss. Journal of Multivariate Analysis (1979): 579588.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): 377416.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): 279284.Google Scholar
4. Davis, A. W.Statistical Distributions in Univariate and Multivariate Edgeworth Populations. Biometrika 63 (1976): 661670.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. 361379. 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): 75106.CrossRefGoogle Scholar
9. Knight, J. L.The Moments of OLS and 2SLS When the Disturbances are Non-normal. Journal of Econometrics 27 (1985): 3960.CrossRefGoogle Scholar
10. Knight, J. L.The Joint Characteristic Function of Linear and Quadratic Forms of Nonnormal Variables. Sankhya A 47 (1985): 231238.Google Scholar
11. Phillips, P.C.B.The Exact Distribution of the Stein-rule Estimator. Journal of Econometrics 25 (1984): 123131.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):521.Google Scholar
14. Ullah, A.On the Sampling Distribution of Improved Estimators for Coefficients in Linear Regression. Journal of Econometrics 2 (1974): 143150.CrossRefGoogle Scholar
15. Ullah, A.The Exact, Large-Sample and Small-disturbance Conditions of Dominance of Biased Estimators in Linear Models. Economic Letters (1980): 339344.CrossRefGoogle Scholar
16. Ullah, A.The Approximate Distribution of the Stein-rule Estimator. Economics Letters 10 (1982): 305308.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): 389402.CrossRefGoogle Scholar