COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION

Deniz Ünal; Güzin Yüksel

Research Article

COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION

Year 2009, Volume: 38 Issue: 3, 351 - 356, 01.03.2009

Abstract

The iterative Stein-rule estimator and the usual estimator of the error variance are compared under the Pitman Nearness Criterion. An exact
expression of Pitman’s Nearness probability is derived and numerically evaluated.

Keywords

Iterative Stein-rule estimator, Pitman Nearness Criterion, Stein-rule estimator, 2000 AMS Classification: 62 J 05

References

James, W. and Stein, C. Estimation with quadratic loss, Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability, 361–379, 1961.
Keating, J. P. and Czitrom, V. A comparison of James-Stein regression with least squares in the Pitman nearness sense, Journal of Statistical Computation and Simulation 34, 1–9, 1989.
Keating, J. P. and Mason,R. L. Closeness comparison of classical and inverse regression estimators, Computational Statistics and Data Analysis 12, 4–11, 1991.
Keating, J. P., Mason, R. L. and Sen, P. K. Pitman’s measure of closeness: a comparison of statistical estimators(Society for Industrial and Applied Mathematics, Philadelphia, 1993).
Ohtani, K. Inadmisibility of the Iterative Stein-rule estimator of the disturbance variance in a linear regression.Economics Letters 24, 51–55, 1987.
Ohtani, K. and Wan, T. K. A. Comparison of the Stein and the usual estimators for the regression error variance under the Pitman nearness Criterion when variables are omitted. Statistical Papers, 10.1007/s00362-007-0047-6, 2007.
Peddada, S. D. A short note on Pitman’s measure of nearness, The American Statistician 39(4), 298–299, 1985.
Pitman, E. J. G. The closest estimates of statistical parameters, Proceedings of the Cam- bridge Philosophical Society 33, 212–222, 1937.
Rao, C. R. Some comments on the minimum mean square error as a criterion of estimation. In: Csorge M, Dawson, D. A., Rao, J. N. K. and Saleh, A. K. MdE (eds) Statistics and related topics(North Holland, Amsterdam, 1981), 123–143.
Unal, D. The effects of the proxy information on the iterative Stein-rule estimator of the
disturbance variance, Statistical Papers, 10.1007/s00362-009-0220-1, 2009

COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION

Year 2009, Volume: 38 Issue: 3, 351 - 356, 01.03.2009

Deniz Ünal Güzin Yüksel

Abstract

References

James, W. and Stein, C. Estimation with quadratic loss, Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability, 361–379, 1961.
Keating, J. P. and Czitrom, V. A comparison of James-Stein regression with least squares in the Pitman nearness sense, Journal of Statistical Computation and Simulation 34, 1–9, 1989.
Keating, J. P. and Mason,R. L. Closeness comparison of classical and inverse regression estimators, Computational Statistics and Data Analysis 12, 4–11, 1991.
Keating, J. P., Mason, R. L. and Sen, P. K. Pitman’s measure of closeness: a comparison of statistical estimators(Society for Industrial and Applied Mathematics, Philadelphia, 1993).
Ohtani, K. Inadmisibility of the Iterative Stein-rule estimator of the disturbance variance in a linear regression.Economics Letters 24, 51–55, 1987.
Ohtani, K. and Wan, T. K. A. Comparison of the Stein and the usual estimators for the regression error variance under the Pitman nearness Criterion when variables are omitted. Statistical Papers, 10.1007/s00362-007-0047-6, 2007.
Peddada, S. D. A short note on Pitman’s measure of nearness, The American Statistician 39(4), 298–299, 1985.
Pitman, E. J. G. The closest estimates of statistical parameters, Proceedings of the Cam- bridge Philosophical Society 33, 212–222, 1937.
Rao, C. R. Some comments on the minimum mean square error as a criterion of estimation. In: Csorge M, Dawson, D. A., Rao, J. N. K. and Saleh, A. K. MdE (eds) Statistics and related topics(North Holland, Amsterdam, 1981), 123–143.
Unal, D. The effects of the proxy information on the iterative Stein-rule estimator of the
disturbance variance, Statistical Papers, 10.1007/s00362-009-0220-1, 2009

There are 11 citations in total.

Details

Primary Language	English
Subjects	Statistics
Journal Section	Mathematics
Authors	Deniz Ünal This is me Güzin Yüksel This is me
Publication Date	March 1, 2009
Published in Issue	Year 2009 Volume: 38 Issue: 3

Cite

APA	Ünal, D., & Yüksel, G. (2009). COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION. Hacettepe Journal of Mathematics and Statistics, 38(3), 351-356.
AMA	Ünal D, Yüksel G. COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION. Hacettepe Journal of Mathematics and Statistics. March 2009;38(3):351-356.
Chicago	Ünal, Deniz, and Güzin Yüksel. “COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION”. Hacettepe Journal of Mathematics and Statistics 38, no. 3 (March 2009): 351-56.
EndNote	Ünal D, Yüksel G (March 1, 2009) COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION. Hacettepe Journal of Mathematics and Statistics 38 3 351–356.
IEEE	D. Ünal and G. Yüksel, “COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION”, Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, pp. 351–356, 2009.
ISNAD	Ünal, Deniz - Yüksel, Güzin. “COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION”. Hacettepe Journal of Mathematics and Statistics 38/3 (March 2009), 351-356.
JAMA	Ünal D, Yüksel G. COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION. Hacettepe Journal of Mathematics and Statistics. 2009;38:351–356.
MLA	Ünal, Deniz and Güzin Yüksel. “COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION”. Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, 2009, pp. 351-6.
Vancouver	Ünal D, Yüksel G. COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION. Hacettepe Journal of Mathematics and Statistics. 2009;38(3):351-6.