Generalization of likelihood ratio tests under nonstandard conditions

Annals of Statistics

Volumn 25, Issue 2, 1997, Pages 897-916

  Vu, H T V ^a   Zhou, S ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Boundary hypothesis tests; Maximum estimators

Indexed keywords

EID: 0031497559     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1031833677     Document Type: Article

References (11)

1. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
2. CHANT, D. (1974). On asymptotic tests of composite hypotheses in nonstandard conditions. Biometrika 61 291-298.
3. CHERNOFF, H. (1954). On the distribution of the likelihood ratio. Ann. Math. Statist. 25 573-578.
4. CROWDER, M. (1990). On some nonregular tests for a modified Weibull model. Biometrika 77 449-506.
5. FAHRMEIR, L. and KAUFMANN, H. (1985). Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. Ann. Statist. 13 342-368.
6. FEDER, P. I. (1968). On the distribution of the log likelihood ratio test statistic when the true parameter is 'near' the boundaries of the hypothesis region. Ann. Math. Statist. 39 2044-2055.
7. GEYER, C. J. (1994). On the asymptotics of constrained M-estimation. Ann. Statist. 22 1993-2010.
8. GHITANY, M. E., MALLER, R. A. and ZHOU, S. (1994). Exponential mixture models with long-term survivors and covariates. J. Multivariate Anal. 49 218-241.
9. MORAN, A. P. (1971). Maximum-likelihood estimation in non-standard conditions. Proc. Cambridge Philos. Soc. 70 441-450.
10. SEARLE, S. R., CASELLA, G. and MCCULLOCH, C. E. (1992). Variance Components. Wiley, New York.
11. SELF, S. G. and LIANG, K. Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Amer. Statist. Assoc. 82 605-610.