Modeling and Inference for Positively Dependent Variables in Dichotomous Experiments

摘要

Multivariate models with positively correlated components have found wide applicability in reliability and biostatistics. Perhaps the best known and most widely used such model is the multivariate exponential distribution due to Marshall and Olkin (JASA, 1967). We study a discrete analogue of the latter model. Specifically, we consider a model for random vecotrs Y whose components are positively correlated and have Bernoulli marginal distributions. The construction ofthe model reflects the fact that the k component system under study may be subjected to independent shocks selectively fatal to any subset of components. A special representation of the probability functon of Y is developed which proves useful in the inference questions pursued. While maximum likelihood estimation of the model parameters proves intractable, we obtain in closed form an alternative estimator which we show to be asymptotically equivalent to the MLE and, in fact, equals the MLE with limiting probability one. Similar results are obtained for a natural submodel whose parameter space is of substantially lower dimension. A Monte Carlo study sheds light on the sample size needed for the asymptotic results to take hold. (Author)