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COMPARISON OF THE ITERATIVE STEIN-RULE AND THE USUAL ESTIMATORS OF THE ERROR VARIANCE UNDER THE PITMAN NEARNESS CRITERION
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.
expression of Pitman’s Nearness probability is derived and numerically evaluated.
Keywords
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.
Details
Primary Language
English
Subjects
Statistics
Journal Section
Research Article
Publication Date
March 1, 2009
Submission Date
May 12, 2014
Acceptance Date
-
Published in Issue
Year 2009 Volume: 38 Number: 3
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. https://izlik.org/JA72LL24ZU
AMA
1.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):351-356. https://izlik.org/JA72LL24ZU
Chicago
Ünal, Deniz, and Güzin Yüksel. 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): 351-56. https://izlik.org/JA72LL24ZU.
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
[1]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, Mar. 2009, [Online]. Available: https://izlik.org/JA72LL24ZU
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 1, 2009): 351-356. https://izlik.org/JA72LL24ZU.
JAMA
1.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, Mar. 2009, pp. 351-6, https://izlik.org/JA72LL24ZU.
Vancouver
1.Deniz Ünal, 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 [Internet]. 2009 Mar. 1;38(3):351-6. Available from: https://izlik.org/JA72LL24ZU