@article {perlman_improved_2006,
	title = {Some Improved Tests for Multivariate One-Sided Hypotheses},
	journal = {Metrika},
	volume = {64},
	number = {1},
	year = {2006},
	month = {feb},
	pages = {23{\textendash}39},
	abstract = {Multivariate one-sided hypothesis-testing problems are very common in clinical trials with multiple endpoints. The likelihood ratio test (LRT) and union-intersection test (UIT) are widely used for testing such problems. It is argued that, for many important multivariate one-sided testing problems, the LRT and UIT fail to adapt to the presence of subregions of varying dimensionalities on the boundary of the null parameter space and thus give undesirable results. Several improved tests are proposed that do adapt to the varying dimensionalities and hence reflect the evidence provided by the data more accurately than the LRT and UIT. Moreover, the proposed tests are often less biased and more powerful than the LRT and UIT.},
	keywords = {Economic Theory, general, likelihood ratio test, Multiple endpoints, One-sided hypothesis, p-value, Probability Theory and Stochastic Processes, Statistics, Statistics for Business/Economics/Mathematical Finance/Insurance, Union-intersection test},
	issn = {0026-1335, 1435-926X},
	doi = {10.1007/s00184-006-0028-0},
	url = {http://link.springer.com/article/10.1007/s00184-006-0028-0},
	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}
}
