The performance of the adaptive optimal estimator under the extended balanced loss function

References

• Chaturvedi, A., and Shalabh 2014. Bayesian estimation of regression coefficients under extended balanced loss function. Communications in Statistics - Theory and Methods 43:4253–64.
   Web of Science ®Google Scholar
• Dwivedi, T. D., and V. K. Srivastava. 1978. On the minimum mean squared error estimators in a regression model. Communications in Statistics - Theory and Methods 7:487–94.
   Web of Science ®Google Scholar
• Farebrother R. W. 1975. The minimum mean square error linear estimator and ridge regression. Technometrics 17:127–28.
   Web of Science ®Google Scholar
• Giles, J. A., D. E. A. Giles, and K. Ohtani. 1996. The exact risks of some pre-test and Stein-type regression estimates under balanced loss. Communications in Statistics - Theory and Methods 25:2901–24.
   Web of Science ®Google Scholar
• Gruber, M. H. J. 2004. The efficiency of shrinkage estimators with respect to Zellner's balanced loss function. Communications in Statistics - Theory and Methods 33:235–49.
   Web of Science ®Google Scholar
• James, W., and C. Stein. 1961. Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability 1:361–79.
   Google Scholar
• Ohtani, K., D. E. A. Giles, and J. A. Giles. 1997. The exact risk performance of a pre-test estimator in a heteroskedastic linear regression model under the balanced loss function. Econometric Reviews 16:119–30.
   Google Scholar
• Ohtani, K. 1998. The exact risk of a weighted average estimator of the OLS and Stein-rule estimators in regression under balanced loss. Statistics & Decisions 16:35–5.
   Google Scholar
• Ohtani, K. 1999. Inadmissibility of the Stein-rule estimator under the balanced loss function. Journal of Econometrics 88:193–201.
   Web of Science ®Google Scholar
• Rao, C. R. 1971. Unified theory of linear estimation. Sankhya A 33:371–94.
   Google Scholar
• Rao, C. R. 1973a. Linear Statistical inference and its applications, 2nd ed. New York, NY: Wiley.
   Google Scholar
• Rao, C. R., H. Toutenburg. 1999. Linear models: Least squares and alternatives. Berlin: Springer-Verlag.
   Google Scholar
• Rodrigues, J., and A. Zellner. 1994. Weighted balanced loss function and estimation of the mean time to failure. Communications in Statistics - Theory and Methods 23:3609–16.
   Web of Science ®Google Scholar
• Schaffrin, B. 1985. A note on linear prediction within a Gauss–Markov model linearized with respect to a random approximation. In Proceedings of the First International Tampere Seminar on Linear Statistical Models and Their Applications, ed. by Pukkila, T., S. Puntanen. Tampere, Finland: Department of Mathematical Sciences/Statistics. A-138, 285–300.
   Google Scholar
• Schaffrin, B. 1986. New estimation/prediction techniques for the determination of crustal deformations in the presence of geophysical prior information. Technometrics 130:361–67.
   Google Scholar
• Schaffrin, B. 1987. Less sensitive tests by introducing stochastic linear hypotheses. In Proceedings of the Second International Tampere Conference in Statistics, eds. by Pukkila, T., S. Puntanen. Tampere, Finland: Department of Mathematical Sciences/Statistics. Report A-184, 647–64.
   Google Scholar
• Shalabh,   1995. Performance of Stein-rule procedure for simultaneous prediction of actual and average values of study variable in linear regression model. Bulletin of the International Statistical Institute 56:1375–90.
   Google Scholar
• Shalabh, H. Toutenburg, and C. Heumann. 2009. Stein-rule estimation under an extended balanced loss function. Journal of Statistical Computation and Simulation 79:1259–73.
   Web of Science ®Google Scholar
• Stahlecker, P., and G. Trenkler. 1985. On heterogeneous versions of the best linear and the ridge estimator. In Proceedings of the First International Tampere Seminar on Linear Statistical Models and Their Applications, ed. by Pukkila, T., S. Puntanen. Tampere, Finland: Department of Mathematical Sciences/Statistics. Report A-138, 301–22.
   Google Scholar
• Theil, H. 1958. Economic forecasts and policy. Amsterdam: North-Holland.
   Google Scholar
• Theil, H. 1971. Principles of econometrics. New York, NY: Wiley.
   Google Scholar
• Toutenburg, H. 1968. Vorhersage im allgemeinen linearen Regressionsmodell mit Zusatzinformation öber die Koeffizienten. Operationsforschung Mathematische Statistik 1:107–20.
   Google Scholar
• Toutenburg, H., and   Shalabh 2005. Estimation of regression coefficients subject to exact linear restrictions when some observations are missing and quadratic error balanced loss function is used. Test 14:385–96.
   Web of Science ®Google Scholar
• Tracy, D. S., and A. K. Srivastava. 1994. Comparison of operational variants of best homogeneous and heterogeneous estimators in linear regression. Communications in Statistics - Theory and Methods 23:2313–22.
   Web of Science ®Google Scholar
• Vinod, H. D., and A. Ullah. 1981. Recent advances in regression methods. New York, NY: Marcel Dekker.
   Google Scholar
• Vinod, H. D. 1976. Simulation and extension of a minimum mean estimator in comparison with Stein's. Technometrics 18:491–96.
   Web of Science ®Google Scholar
• Vinod, H. D. 1980. Improved Stein-rule estimator for regression problems. Journal of Econometrics 12:143–50.
   Web of Science ®Google Scholar
• Wan, A. T. K., and A. Chaturvedi. 2000. Operational variants of the minimum mean squared error estimator in linear regression models with non-spherical disturbances. The Annals of Mathematical Statistics 52:332–42.
   Google Scholar
• Zellner, A. 1994. Statistical decision theory and related topics V. Chapter 4, Bayesian and non-Bayesian estimation using balanced loss functions, 377–90, New York, NY: Springer-Verlag.
   Google Scholar