Small sample inference for probabilistic index models

Probabilistic index models may be used to generate classical and new rank tests, with the additional advantage of supplementing them with interpretable effect size measures. The popularity of rank tests for small sample inference makes probabilistic index models also natural candidates for small sample studies. However, at present, inference for such models relies on asymptotic theory that can deliver poor approximations of the sampling distribution if the sample size is rather small. A bias-reduced version of the bootstrap and adjusted jackknife empirical likelihood are explored. It is shown that their application leads to drastic improvements in small sample inference for probabilistic index models, justifying the use of such models for reliable and informative statistical inference in small sample studies

A goodness-of-fit test for parametric and semi-parametric models in multiresponse regression

We propose an empirical likelihood test that is able to test the goodness of fit of a class of parametric and semi-parametric multiresponse regression models. The class includes as special cases fully parametric models; semi-parametric models, like the multiindex and the partially linear models; and models with shape constraints. Another feature of the test is that it allows both the response variable and the covariate be multivariate, which means that multiple regression curves can be tested simultaneously. The test also allows the presence of infinite-dimensional nuisance functions in the model to be tested. It is shown that the empirical likelihood test statistic is asymptotically normally distributed under certain mild conditions and permits a wild bootstrap calibration. Despite the large size of the class of models to be considered, the empirical likelihood test enjoys good power properties against departures from a hypothesized model within the class.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ208 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Stochastic Ordering under Conditional Modelling of Extreme Values: Drug-Induced Liver Injury

Drug-induced liver injury (DILI) is a major public health issue and of serious concern for the pharmaceutical industry. Early detection of signs of a drug's potential for DILI is vital for pharmaceutical companies' evaluation of new drugs. A combination of extreme values of liver specific variables indicate potential DILI (Hy's Law). We estimate the probability of severe DILI using the Heffernan and Tawn (2004) conditional dependence model which arises naturally in applications where a multidimensional random variable is extreme in at least one component. We extend the current model by including the assumption of stochastically ordered survival curves for different doses in a Phase 3 study.Comment: 24 pages, 5 figure