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Journals / Hacettepe Journal of Mathematics and Statistics / 2009 / Volume: 38 Issue: 3

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

Deniz Ünal
Güzin Yüksel
Pages
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Publication Date
2009-03-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

An exact expression of Pitman’s Nearness probability is derived and numerically evaluated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The iterative Stein-rule estimator and the usual estimator of the error variance are compared under the Pitman Nearness Criterion.
📊
Key Findings & Data:The iterative Stein-rule estimator and the usual estimator of the error variance are compared under the Pitman Nearness Criterion.
💡
Conclusion & Impact:An exact expression of Pitman’s Nearness probability is derived and numerically evaluated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Iterative Stein-rule estimator · Pitman Nearness Criterion · Stein-rule estimator

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.

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Cite This Article

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, Volume: 38 Issue: 3. https://ajindex.com/articles/1403744

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References (11)

  1. James, W. and Stein, C. Estimation with quadratic loss, Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability, 361–379, 1961.
  2. 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.
  3. Keating, J. P. and Mason,R. L. Closeness comparison of classical and inverse regression estimators, Computational Statistics and Data Analysis 12, 4–11, 1991.
  4. 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).
  5. Ohtani, K. Inadmisibility of the Iterative Stein-rule estimator of the disturbance variance in a linear regression.Economics Letters 24, 51–55, 1987.
  6. 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.
  7. Peddada, S. D. A short note on Pitman’s measure of nearness, The American Statistician 39(4), 298–299, 1985.
  8. Pitman, E. J. G. The closest estimates of statistical parameters, Proceedings of the Cam- bridge Philosophical Society 33, 212–222, 1937.
  9. 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.
  10. Unal, D. The effects of the proxy information on the iterative Stein-rule estimator of the
  11. disturbance variance, Statistical Papers, 10.1007/s00362-009-0220-1, 2009