Abstract
In this paper we consider the double k-class estimator which incorporates the Stein variance estimator. This estimator is called the SVKK estimator. We derive the explicit formula for the mean squared error (MSE) of the SVKK estimator for each individual regression coefficient. It is shown analytically that the MSE performance of the Stein-rule estimator for each individual regression coefficient can be improved by utilizing the Stein variance estimator. Also, MSE’s of several estimators included in a family of the SVKK estimators are compared by numerical evaluations.
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References
Berry, J.C. (1994), Improving the James-Stein estimator using the Stein variance estimator, Statistics and Probability Letters, 20, 241–245.
Farebrother, R.W. (1975), The minimum mean square error linear estimator and ridge regression, Technometrics, 17, 127–128.
George, E.I. (1990), Comment on “Decision theoretic variance estimation,” by Maata and Casella, Statistical Science, 5, 107–109.
James, W. and C. Stein (1961), Estimation with quadratic loss, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability I, (Berkeley, University of California Press), 361–379.
Judge G. and T. Yancey (1986), Improved Methods of Inference in Econometrics, (North-Holland, Amsterdam).
Ohtani, K. (1996a), On an adjustment of degrees of freedom in the minimum mean squared error estimator, Communications in Statistics-Theory and Methods, 25, 3049–3058.
Ohtani, K. (1996b), Further improving the Stein-rule estimator using the Stein variance estimator in a misspecified linear regression model, Statistics and Probability Letters, 29, 191–199.
Ohtani, K. (1997), Minimum mean squared error estimation of each individual coefficient in a linear regression model, Journal of Statistical Planning and Inference, 62, 301–316.
Ohtani, K. and H. Kozumi (1996), The exact general formulae for the moments and the MSE dominance of the Stein-rule and positive-part Stein-rule estimators, Journal of Econometrics, 74, 273–287.
Ohtani, K and A.T.K. Wan (1999), On the use of the Stein variance estimator in the double k-class estimator in regression, Econometric Reviews, forthcoming.
Rao, C.R. and N. Shinozaki (1978), Precision of individual estimators in simultaneous estimation of parameters, Biometrika, 65, 23–30.
Stein, C. (1956), Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, (Berkeley, University of California Press), 197–206.
Stein, C. (1964), Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean, Annals of the Institute of Statistical Mathematics, 16, 155–160.
Theil, H. (1971), Principles of Econometrics, (John Wiley, New York).
Ullah, A. and S. Ullah (1978), Double k-class estimators of coefficients in linear regression, Econometrica, 46, 705–722.
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The author is grateful to Kazuhiro Ohtani, Götz Trenkler and anonymous referees for their valuable comments and suggestions.
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Namba, A. On the use of the Stein variance estimator in the double k-class estimator when each individual regression coefficient is estimated. Statistical Papers 44, 117–124 (2003). https://doi.org/10.1007/s00362-002-0137-4
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DOI: https://doi.org/10.1007/s00362-002-0137-4