Estimation and testing in constrained covariance component models

Biometrika

Volumn 84, Issue 1, 1997, Pages 95-102

  Shaw, Frank H ^a   Geyer, Charles J ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Asymptotic parametric bootstrap; Cutting plane algorithm; Semi infinite programming; Variance component

Indexed keywords

EID: 0002479894     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/84.1.95     Document Type: Article

References (21)

1. AITCHISON, J. & SILVEY, S. D. (1958). Maximum likelihood estimation of parameters subject to restraints. Ann. Math. Statist. 29, 813-28.
2. BERAN, R. (1988). Prepivoting test statistics: A bootstrap view of asymptotic refinements. J. Am. Statist. Assoc. 83, 687-97.
3. CALLANAN, T. P. & HARVTLLE, D. A. (1989). Some new algorithms for computing maximum likelihood estimates of variance components. In Computer Science and Statistics: Proceedings of the 21st Symposeum on the Interface, Ed. K. Berk and L. Malone, pp. 435-44. Alexandria, VA: Am. Statist. Assoc.
4. CHERNOFF, H. (1954). On the distribution of the likelihood ratio. Ann. Math. Statist. 25, 573-8.
5. EFRON, B. (1979). Bootstrap methods: Another look at the jackknife. Ann. Statist. 7, 1-26.
6. FALCONER, D. S. (1989). Introduction to Quantitative Genetics. London: Longman.
7. FLETCHER, R. (1987). Practical Methods of Optimization, 2nd ed. Chichester: John Wiley.
8. GEYER, C. J. (1991). Constrained maximum likelihood exemplified by isotonic convex logistic regression. J. Am. Statist. Assoc. 86, 717-24.
9. GEYER, C. J. (1994). On the asymptotics of constrained M-estimation. Ann. Statist. 22, 1993-2010.
10. HARVTLLE, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems (with Discussion). J. Am. Statist. Assoc. 72, 320-40.
11. HETTICH, R. (1983). A review of numerical methods for semi-infinite optimization. In Semi-Infinite Programming and Applications: An International Symposium, Austin, Texas, September 8-10, 1981, Ed. A. V. Fiacco and K. O. Kortanek, pp. 158-78. Berlin: Springer-Verlag.
12. HILL, W. G. & THOMPSON, R. (1978). Probabilities of non-positive definite between group or genetic covariance matrices. Biometrics 34, 429-40.
13. HORST, R. & TUY, H. (1990). Global Optimization: Deterministic Approaches. Berlin: Springer-Verlag.
14. LANDE, R. (1979). Quantitative genetic analysis of multivariate evolution, applied to the brain: bodysize allometry. Evolution 33, 402-16.
15. LECAM, L. (1970). On the assumptions used to prove asymptotic normality of maximum likelihood estimates. Ann. Math. Statist. 41, 802-28.
16. NEWTON, M. A. & GEYER, C. J. (1994). Bootstrap recycling: A Monte Carlo alternative to the nested bootstrap. J. Am. Statist. Assoc. 89, 905-12.
17. ROBERTSON, T., WRIGHT, F. T. & DYKSTRA, R. L. (1988). Order Restricted Inference. Chichesten John Wiley.
18. SEARLE, S. R., CASELLA, G. & MCCULLOCH, C. E. (1993). Variance Components. New York: John Wiley.
19. SELF, S. G. & LIANG, K.-Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Am. Statist. Assoc. 82, 605-10.
20. SHAW, R. G., PLATENKAMP, G. A. J., SHAW, F. H. & PODOLSKY, R. H. (1995). Quantitative genetics of response to competitors in Nemophila menziesii: a field experiment. Genetics 139, 397-406.
21. WILKS, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Statist. 9, 60-2.