James-stein-type estimators in large samples with application to the least absolute deviations estimator

Journal of the American Statistical Association

Volumn 96, Issue 454, 2001, Pages 697-705

  Kim, Tae Hwan ^a   White, Halbert ^b  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Asymptotic risk; Combination estimator; Shrinkage

Indexed keywords

EID: 1542678344     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1198/016214501753168352     Document Type: Article

References (21)

1. Arthanari, T. S., and Dodge, Y. (1982), Mathematical Programming in Statistics, New York: Wiley.
2. Barrodale, I., and Roberts, F. D. K. (1974), “Algorithm 478: Solution of an Over-Determined System of Equations in the L1 Norm,” Communications of the Association for Computing Machinery, 17, 319–320.
3. Bates, C. E., and White, H. (1993), “Determination of Estimators with Minimum Asymptotic Covariance Matrices,” Econometric Theory, 9, 633–648.
4. Breiman, L. (1995), “Better Subset Regression Using the Nonnegative Garrotte,” Technometrics, 37, 373–384.
5. Breiman, L. (1996), “Heuristics of Instability and Stabilization in Model Selection,” The Annals of Statistics, 24, 2350–2383.
6. Cohen, A. (1976), “Combining Estimates of Location,” Journal of the American Statistical Association, 71, 172–175.
7. Green, E. J., and Strawderman W. E. (1991), “James–Stein–Type Estimator for Combining Unbiased and Possibly Biased Estimators,” Journal of the American Statistical Association, 86, 1001–1006.
8. James, W., and Stein, C. (1960), “Estimation With Quadratic Loss,” in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1), Berkeley, CA: University of California Press, pp. 361–379.
9. Judge, G. G., and Bock, M. E. (1978), The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics, Amsterdam: North-Holland.
10. Laplace, P. S. de (1818), Deuxieme Supplement a la Theorie Analytique des Probabilites. Networks. Reprinted (1847) in Oeuvres Completes de Laplace, vol. 7. Paris: Gauthier-Villars, pp. 531–580.
11. Saleh, A. K. M. E., and Han, C. P. (1990), “Shrinkage Estimation in Regression Analysis,” Estadistica, 42, 40–63.
12. Saleh, A. K. M. E., and Sen, P. K. (1985a), “On Shrinkage M-Estimators of Location Parameters,” Communications in Statistics, Part A—Theory and Methods, 14, 2313–2329.
13. Saleh, A. K. M. E., and Sen, P. K. (1985b), “On Some Shrinkage Estimators of Multivariate Location,” The Annals of Statistics, 13, 272–281.
14. Saleh, A. K. M. E., and Sen, P. K. (1986), “On Shrinkage R-Estimation in a Multiple Regression Model,” Communications in Statistics: Part A—Theory and Methods, 15, 2229–2244.
15. Saleh, A. K. M. E., and Sen, P. K. (1987a), “Relative Performance of Stein-Rule and Preliminary Test Estimators in Linear Models: Least Squares Theory,” Communications in Statistics: Part A—Theory and Methods, 16, 461–476.
16. Saleh, A. K. M. E., and Sen, P. K. (1987b), “On the Asymptotic Distributional Risk Properties of Pre-Test and Shrinkage L1-Estimators,” Computational Statistics & Data Analysis, 5, 289–299.
17. Schmoyer, R., and Arnold, S. (1989), “Shrinking Techniques for Robust Regression,” in Contributions to Probability and Statistics: Essays in Honor of Ingram Olkin, ed. L. J. Gleser, New York: Springer-Verlag, pp. 368–384.
18. Sen, P. K., and Saleh, A. K. M. E. (1987), “On Preliminary Test and Shrinkage M-Estimation in Linear Models,” The Annals of Statistics, 15, 1580–1592.
19. Stein, C. (1955), “Inadmissibility of the Usual Estimator for the Mean of a Multivariate Distribution,” in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1), Berkeley, CA: University of California Press, pp. 197–206.
20. Taylor, L. D. (1974), “Estimation by Minimizing the Sum of Absolute Errors,” in Frontiers in Econometrics, ed. P. Zarembka, New York: Academic Press.
21. Ullah, A. (1990), “Finite Sample Econometrics: A Unified Approach,” in Contributions to Econometric Theory and Application: Essays in Honour of A. L. Nagar, eds. R. A. L. Carter, J. Dutta, and A. Ullah, New York: Springer-Verlag, pp. 242–292.