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Inadmissibility of the Stein-rule estimator under the balanced loss function. (English) Zbl 0933.62008

Summary: The risk of the Stein-rule (SR) estimator is compared with that of the improved Stein-rule estimator using the Stein variance (SRSV) estimator under the balanced loss function. It is shown that the SRSV estimator dominates the SR estimator even if the loss function is extended to the balanced loss function (BLF). Also, our numerical results show that the SRSV estimator dominates the OLS estimator when the weight of precision of estimation is larger than about half, and vice versa.

MSC:

62C15 Admissibility in statistical decision theory
62J05 Linear regression; mixed models
62P20 Applications of statistics to economics
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[1] Baranchik, A. J.: A family of minimax estimators of the mean of a multivariate normal distribution. Annals of mathematical statistics 41, 642-645 (1970)
[2] Berry, J. C.: Improving the James–Stein estimator using the Stein variance estimator. Statistics and probability letters 20, 241-245 (1994) · Zbl 0801.62059
[3] Gelfand, A. E.; Dey, D. K.: Improved estimation of the disturbance variance in a linear regression model. Journal of econometrics 39, 387-395 (1988) · Zbl 0677.62060
[4] George, E. I.: Comments on ‘decision theoretic variance estimation’, by maata and casella. Statistical science 5, 107-109 (1990)
[5] Giles, J. A.; Giles, D. E. A.: Preliminary test estimation of the regression scale parameter when the loss function is asymmetric. Communications in statistics-theory and methods 22, 1709-1733 (1993) · Zbl 0784.62057
[6] Giles, J. A.; Giles, D. E. A.; Ohtani, K.: The exact risk of some pre-test and Stein-type regression estimators under balanced loss. Communications in statistics-theory and methods 25, 2901-2924 (1995) · Zbl 0901.62086
[7] James, W., Stein, C., 1961. Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1, University of California Press, Berkeley, pp. 361–379. · Zbl 1281.62026
[8] Ohtani, K.: Generalized ridge regression estimators under the LINEX loss function. Statistical papers 36, 99-110 (1995) · Zbl 0820.62064
[9] Ohtani, K.: Further improving the Stein-rule estimator using the Stein variance estimator in a misspecified linear regression model. Statistics and probability letters 29, 191-199 (1996) · Zbl 0861.62055
[10] Ohtani, K.; Kozumi, H.: 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 (1996) · Zbl 1127.62381
[11] Rodrigues, J.; Zellner, A.: Weighted balanced loss function and estimation of the mean time to failure. Communications in statistics-theory and methods 23, 3609-3616 (1994) · Zbl 0825.62250
[12] 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 1, University of California Press, Berkeley, pp. 197–206. · Zbl 0073.35602
[13] Stein, C.: 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 (1964) · Zbl 0144.41405
[14] Varian, H.R., 1975. A Bayesian approach to real estate assessment. In: Fienberg, S.E., Zellner, A. (Eds.), Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage, North-Holland, Amsterdam, pp. 195–208.
[15] Wan, A. T. K.: Risk comparison of the inequality constrained least squares and other related estimators under balanced loss. Economics letters 46, 203-210 (1994) · Zbl 0875.62591
[16] Zellner, A.: Bayesian estimation and prediction using asymmetric loss functions. Journal of the American statistical association 81, 446-451 (1986) · Zbl 0603.62037
[17] Zellner, A., 1994. Bayesian and non-Bayesian estimation using balanced loss functions. In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics V, Springer-Verlag, Berlin, pp. 377–390. · Zbl 0787.62035
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