@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}
}
@article {perlman_class_2002,
title = {A class of conditional tests for a multivariate one-sided alternative},
journal = {Journal of Statistical Planning and Inference},
volume = {107},
number = {1{\textendash}2},
year = {2002},
pages = {155{\textendash}171},
abstract = {Consider testing H0: μ1=...=μp=0 versus the multivariate one-sided alternative H1: μ1⩾0,{\textellipsis},μp⩾0 based on a sample from a p-dimensional normal distribution Np(μ,Σ) with Σ unknown, where μ=(μ1,{\textellipsis},μp). Perlman (Ann. Math. Statist. 40 (1969) 549) obtained the likelihood ratio test (LRT) statistic and its null distribution, while Shorack (Ann. Math. Statist. 38 (1967) 1740) and Silvapulle (J. Multivariate Anal. 55 (1995) 312) studied an alternative test statistic. Neither test is similar, however, hence both are biased, and neither dominates the other in terms of power. Tang (J. Am. Statist. Assoc. 89 (1994) 1006) proposed a test that is similar, unbiased, and everywhere more powerful than the original LRT. Here we study a new class of conditional tests based on the LRT statistic and obtain the conditional test that is most nearly similar within this class. The resulting test is more powerful than the LRT for most alternatives, is not dominated in power by Tang{\textquoteright}s test, and is more convenient to apply. Furthermore, unlike Tang{\textquoteright}s test, the conditional test always accepts H0 when μ̂=(μ̂1,{\textellipsis},μ̂p)=(0,{\textellipsis},0), where μ̂ is the MLE of μ under H1. Similar results are found for a conditional version of the Shorack{\textendash}Silvapulle test.},
keywords = {Conditional test, likelihood ratio test, Multivariate normal distribution, One-sided alternative, Tests for means},
issn = {0378-3758},
doi = {10.1016/S0378-3758(02)00250-1},
url = {http://www.sciencedirect.com/science/article/pii/S0378375802002501},
author = {Perlman, Michael D. and WU, LANG}
}
@article {wu_testing_2000,
title = {Testing lattice conditional independence models based on monotone missing data},
journal = {Statistics \& Probability Letters},
volume = {50},
number = {2},
year = {2000},
month = {nov},
pages = {193{\textendash}201},
abstract = {Lattice conditional independence (LCI) models (Anderson and Perlman, 1991. Statist. Probab. Lett. 12, 465{\textendash}486; 1993 Ann. Statist. 21, 1318{\textendash}1358) can be applied to the analysis of missing data problems with non-monotone missing patterns. Closed-form maximum likelihood estimates can always be obtained under the LCI models naturally determined by the observed data patterns. In practice, it is important to test the appropriateness of LCI models. In the present paper, we derive explicit likelihood ratio tests for testing LCI models based on a monotone subset of the observed data.},
keywords = {likelihood ratio test, Multivariate normal data, Restricted maximum likelihood estimates},
issn = {0167-7152},
doi = {10.1016/S0167-7152(00)00098-5},
url = {http://www.sciencedirect.com/science/article/pii/S0167715200000985},
author = {WU, LANG and Perlman, Michael D.}
}
@article {perlman_emperors_1999,
title = {The Emperor{\textquoteright}s new tests},
journal = {Statistical Science},
volume = {14},
number = {4},
year = {1999},
month = {nov},
pages = {355{\textendash}369},
abstract = {In the past two decades, striking examples of allegedly inferior likelihood ratio tests (LRT) have appeared in the statistical literature. These examples, which arise in multiparameter hypothesis testing problems, have several common features. In each case the null hypothesis is composite, the size LRT is not similar and hence biased, and competing size tests can be constructed that are less biased, or even unbiased, and that dominate the LRT in the sense of being everywhere more powerful. It is therefore asserted that in these examples and, by implication, many other testing problems, the LR criterion produces {\textquoteleft}{\textquoteleft}inferior,{\textquoteright}{\textquoteright} {\textquoteleft}{\textquoteleft}deficient,{\textquoteright}{\textquoteright} {\textquoteleft}{\textquoteleft} undesirable,{\textquoteright}{\textquoteright} or {\textquoteleft}{\textquoteleft}flawed{\textquoteright}{\textquoteright} statistical procedures. This message, which appears to be proliferating, is wrong. In each example it is the allegedly superior test that is flawed, not the LRT. At worst, the {\textquoteleft}{\textquoteleft}superior{\textquoteright}{\textquoteright} tests provide unwarranted and inappropriate inferences and have been deemed scientifically unacceptable by applied statisticians. This reinforces the well-documented but oft-neglected fact that the Neyman-Pearson theory desideratum of a more or most powerful size test may be scientifically inappropriate; the same is true for the criteria of unbiasedness and -admissibility. Although the LR criterion is not infallible, we believe that it remains a generally reasonable first option for non-Bayesian parametric hypothesis-testing problems.},
keywords = {a-admissibility, bioequivalence problem, d-admissibility, Fisher-Neyman debate, Hypothesis test, likelihood ratio test, multiple endpoints in clinical trials, multivariate one-sided alternatives, order-restricted hypotheses, power, significance test, size test, test for qualitative interactions, unbiased test},
issn = {0883-4237, 2168-8745},
doi = {10.1214/ss/1009212517},
url = {http://projecteuclid.org/euclid.ss/1009212517},
author = {Perlman, Michael D. and WU, LANG}
}