@article {perlman_note_2004,
title = {A Note on One-Sided Tests with Multiple Endpoints},
journal = {Biometrics},
volume = {60},
number = {1},
year = {2004},
month = {mar},
pages = {276{\textendash}280},
abstract = {Summary.~ Testing problems with multivariate one-sided alternative hypotheses are common in clinical trials with multiple endpoints. In the case of comparing two treatments, treatment 1 is often preferred if it is superior for at least one of the endpoints and not biologically inferior for the remaining endpoints. Bloch et al. (2001, Biometrics57, 1039{\textendash}1047) propose an intersection{\textendash}union test (IUT) for this testing problem, but their test does not utilize the appropriate multivariate one-sided test. In this note we modify their test by an alternative IUT that does utilize the appropriate one-sided test. Empirical and graphical evidence show that the proposed test is more appropriate for this testing problem.},
keywords = {Hotelling{\textquoteright}s T~2, Intersection-union test, Likelihood ratio tests, Multiple endpoints, Multivariate one-sided test},
issn = {1541-0420},
doi = {10.1111/j.0006-341X.2004.00159.x},
url = {http://onlinelibrary.wiley.com/doi/10.1111/j.0006-341X.2004.00159.x/abstract},
author = {Perlman, Michael D. and WU, LANG}
}
@article {perlman_validity_2003,
title = {On the validity of the likelihood ratio and maximum likelihood methods},
journal = {Journal of Statistical Planning and Inference},
volume = {117},
number = {1},
year = {2003},
month = {nov},
pages = {59{\textendash}81},
abstract = {When the null or alternative hypothesis of a statistical testing problem is a union of finitely many regions of varying dimensionality, the likelihood ratio test is statistically inappropriate. Its inappropriateness is revealed not by its performance under the Neyman{\textendash}Pearson criterion but by the fact that it yields incorrect inferences in certain regions of the sample space due to its inability to adapt to the differing dimensions in the composite hypothesis. Maximum likelihood estimators and associated model selection procedures also are inappropriate for such composite models. Tests and estimators based on the p-values associated with each of the regions that constitute the composite model are more appropriate for this geometry. Similar issues arise when the boundary of the null hypothesis is a union of finitely many regions of varying dimensionality.},
keywords = {Intersection-union test, likelihood ratio test, Model selection, Non-nested hypotheses, Union-intersection test, Varying dimensionality},
issn = {0378-3758},
doi = {10.1016/S0378-3758(02)00359-2},
url = {http://www.sciencedirect.com/science/article/pii/S0378375802003592},
author = {Perlman, Michael D. and WU, LANG}
}