Estimation of a normal variance - A critical review

Statistical Papers

Volumn 39, Issue 4, 1998, Pages 389-404

  Pal, Nabendu ^a   Ling, Chiahua ^c   Lin, Jyh Jiuan ^b  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

^b China Jr Coll Indust Comml Mgmt   (Taiwan)

^c Tahan Junior College   (Taiwan)

Author keywords

Affine equivariance; Loss function; Minimax estimator; Risk function

Indexed keywords

EID: 0542445417     PISSN: 09325026     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02927101     Document Type: Review

References (18)

1. Abramowitz, M. and Stegun, I. A. (1968). Handbook of Mathematical Functions. US Department of Commerce, Washington D. C.
2. Brewster, J. F. and Zidek, J. V. (1974). Improving on equivariant estimators. Annals of Statistics, 2, 21-38.
3. Brown, L. D. (1968). Inadmissibility of the usual estimators of scale parameters in problems with unknown location and scale parameters. Annals of Mathematical Statistics, 39, 29-48.
4. Brown, L. D. (1986). Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory. Institute of Mathematical Statistics (Lecture Notes-Monograph Series, Volume - 9).
5. Ghosh, M. (1994). On some Bayesian solutions of the Neyman - Scott problem. Proceedings of the Purdue Symposium on Decision Theory & Bayesian Analysis.
6. Guo, Y. Y. and Pal, N. (1992). A sequence of improvements over the James-Stein estimator. Journal of Multivariate Analysis, 42, No. 2, 302-317.
7. Kubokawa, T. (1994). A unified approach to improving equivariant estimators. Annals of Statistics, 22, 290-299.
8. Ling, C. (1995). Some results on normal scale parameter estimation. Ph.D. dissertation, University of Southwestern Louisiana, Lafayette, Louisiana, USA.
9. Maatta, J. M. and Casella, G. (1990). Developments in decision-theoretic variance estimation. Statistical Science, 5, 90-120.
10. Neyman, J. and Scott, E. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16, 1-32.
11. Pal, N. and Ling, C. (1995). Improved estimation of powers of the variance of a multivariate normal distribution under entropy loss function. Statistics & Probability Letters, 24, 205-211.
12. Pal, N. and Ling, C. (1996). Estimation of a normal scale parameter under a balanced loss function. Journal of the Indian Statistical Association, 34, 21-38.
13. Proskin, H. M. (1985). An admissibility theorem with applications to the estimation of the variance of the normal distribution. Ph. D. dissertation, Dept. of Statistics, Rutgers University.
14. Rukhin, A. L. (1987). How much better are better estimators of a normal variance? Journal of the American Statistical Association, 82, 925-928.
15. Rukhin, A. L. and Ananda, M. M. A. (1992). Risk behavior of variance estimators in multivariate normal distribution. Statistics & Probability Letters, 13, 159-166.
16. Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. John Wiley & Sons, New York.
17. Stein, C. (1964). 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.
18. Strawderman, W. E. (1974). Minimax estimation of powers of the variance of a normal population under squared error loss. Annals of Statistics, 2, 190-198.