The exact risks of some pre-test and stein-type regression estimators under balanced loss

Communications in Statistics - Theory and Methods

Volumn 25, Issue 12, 1996, Pages 2901-2924

  Giles, Judith A ^a   Giles, David E A ^a   Ohtani, Kazuhiro ^b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b KOBE UNIVERSITY   (Japan)

Author keywords

Conditional inference; Estimation precision; Goodness of fit; Linear regression; Shrinkage estimators

Indexed keywords

EID: 0042543768     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1080/03610929608831878     Document Type: Article

References (29)

1. Bancroft, T.A. (1944). "On biases in estimation due to the use of preliminary tests of significance," Annals of Mathematical Statistics, 15, 190-204.
2. Baranchik, A.J. (1964). "Multiple regression and estimation of the mean of a multivariate normal distribution," Technical Report No. 51, Department of Statistics, Stanford University.
3. Brook, R.J. (1976). "On the use of a regret function to set significance points in prior tests of estimation," Journal of the American Statistical Association, 71, 126-131.
4. Clarke, J.A., Giles, D.E.A. and Wallace, T.D. (1987). "Estimating the error variance in regression after a preliminary test of restrictions on the coefficients," Journal of Econometrics, 34, 293-304.
5. Cohen, A. (1965). "Estimates of the linear combinations of parameters in the mean vector of a multivariate distribution," Annals of Mathematical Statistics, 36, 299-304.
6. Cunneen, M.C. and Giles, J.A. (1994). "Autocorrelation pre-testing using a balanced loss function," mimeo., Department of Economics, University of Victoria.
7. Ghosh, M., Saleh, A.K.Md.E. and Sen, P.K. (1989). "Empirical Bayes subset estimation in regression models," Statistics and Decisions, 7, 15-35.
8. Ghosh, M., Lee, L.C. and Littell, R.C. (1990). "Empirical and hierarchical Bayes estimation of the response function," Statistics and Decisions, 8, 299-330.
9. Giles, D.E.A. (1993). "Pre-test estimation in regression under absolute error loss," Economics Letters, 41, 339-343.
10. Giles, J.A. and Giles, D.E.A. (1993a). "Preliminary-test estimation of the regression scale parameter when the loss function is asymmetric," Communications in Statistics: Theory and Methods, A22, 1709-1734.
11. Giles, J.A. and Giles, D.E.A. (1993b). "Pre-test estimation and testing in econometrics: Recent developments," Journal of Economic Surveys, 7, 145-196.
12. Giles, J.A. and Giles, D.E.A. (1996). "Risk of a homoskedasticity pre-test estimator of the regression scale under LINEX loss," Journal of Statistical Planning and Inference, 50, 21-35.
13. James, W. and Stein, C. (1961). "Estimation with quadratic loss," Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley: University of California Press, 361-379.
14. Judge, G.G. and Bock, M.E. (1978). The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics, Amsterdam: North-Holland.
15. Judge, G.G., Yancey, T.A. and Bock, M.E. (1983). "Pre-test estimation under squared error loss," Economics Letters, 11, 347-352.
16. Ohtani, K. (1993). "A comparison of the Stein-rule and positive part Stein-rule estimators in a misspecified linear regression model," Econometric Theory, 9, 668-679.
17. Ohtani, K., Giles, D.E.A. and Giles, J.A. (1993). "The risk behaviour of a pre-test estimator in a regression model with possible heteroskedasticity under the LINEX loss function," mimeo., Faculty of Economics, Kobe University.
18. Ohtani, K., Giles, D.E.A. and Giles, J.A. (1996). "The exact risk performance of a pre-test estimator in a heteroskedastic linear regression model under the balanced loss function," Econometric Reviews, forthcoming.
19. Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1986). Numerical Recipes: The Art of Scientific Computing, Cambridge: Cambridge University Press.
20. Rodrigues, J. and Zellner, A. (1994). "Weighted balanced loss function and estimation of the mean time to failure," Communications in Statistics: Theory and Methods, A23, 3609-3612.
21. 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, Vol. 1, Berkeley: University of California Press, 197-206.
22. Stein, C. (1966). "An approach to the recovery of inter-block information on balanced incomplete block designs," Research Papers in Statistics, (F. N. David, Ed.). New York: Wiley, 351-366.
23. Toro-Vizcarrondo, C. and Wallace, T.D. (1968). "A test of the mean square error criterion for restrictions in linear regression," Journal of the American Statistical Association, 63, 558-572.
24. Varian, H. (1974). "A Bayesian approach to real estate assessment," Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage, Vol. 1, Amsterdam: North-Holland, 195-208.
25. Wan, A.T.K. (1994). "Risk comparisons of the inequality constrained least squares and other related estimators under balanced loss," Economics Letters, 46, 203-210.
26. Zellner, A. (1986a). "Further results on Bayesian minimum expected loss (MELO) estimates and posterior distributions for structural coefficients," Advances in Econometrics, Vol. 5, (D. Slottje, Ed.). Greenwich CT: JAI Press, 171-182.
27. Zellner, A. (1986b). "Bayesian estimation and prediction using asymmetric loss functions," Journal of the American Statistical Association, 81, 446-451.
28. Zellner, A. (1994). "Bayesian and non-Bayesian estimation using balanced loss functions," Statistical Decision Theory and Related Topics, V, (S.S. Gupta and J.O. Berger, Eds.). New York: Springer-Verlag, 377-390.
29. Zellner, A. (1996). "The finite sample properties of simultaneous equations' estimates and estimators: Bayesian and non-Bayesian approaches," Journal of Econometrics, forthcoming.