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

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

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

___

  • 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