The authors consider copula models for vectors of binary response variables having marginal distributions that depend on covariates through logistic regressions. They show how to test for residual pairwise dependence between responses, given the explanatory variables. The procedure they propose is based on the score statistic derived from the assumed copula structure under the alternative. The authors further argue that conditional dependence can be conveniently modelled with meta-elliptical copulas, which offer a wide range of positive and negative degrees of association. They call on a composite likelihood to estimate the copula parameters and they provide standard error estimates of the same via linearization. They illustrate their results with Canadian data on the presence or absence of various log grades in trees.

We consider methods for constructing multivariate dispersion models, illustrated by examples. Such methods are motivated by the need for good regression modelling of multivariate nonnormal correlated data, which requires multivariate distributions with a flexible correlation structure. We first review existing methods for constructing multivariate proper dispersion models, involving quadratic forms of deviance residuals in the style of the multivariate normal density, which we illustrate by a multivariate hyperbola distribution. We develop an extended convolution method for constructing multivariate exponential dispersion models, designed to create a fully flexible covariance structure, which we illustrate by two bivariate gamma distributions. We develop a similar technique for constructing multivariate extreme dispersion models for extremes and survival data, and introduce new bivariate logistic and Gumbel distributions.

Necessary and sufficient conditions are derived on the parameters of a $d$-dimensional random vector with Marshall–Olkin distribution to be extendible to an infinite exchangeable sequence. Interpreted differently, this result allows to decide if the respective multivariate exponential distribution can be constructed by means of a model with conditionally independent and identically distributed components. The proof makes use of the solution of the truncated Hausdorff moment problem and a reparameterization of the Marshall–Olkin distribution.

In this work, we derive the copulas related to Manneville–Pomeau processes. We examine both bidimensional and multidimensional cases and derive some properties for the related copulas. Computational issues, approximations and random variate generation problems are addressed and simple numerical experiments to test the approximations developed are also performed. In particular, we propose an approximation to the derived copulas which we show to converge uniformly to the true one. To illustrate the usefulness of the theory, we derive a fast procedure to estimate the underlying parameter in Manneville–Pomeau processes.

Polyhazard models constitute a flexible family for fitting lifetime data. The main advantages over single hazard models include the ability to represent hazard rate functions with unusual shapes and the ease of including covariates. The primary goal of this paper was to include dependence among the latent causes of failure by modeling dependence using copula functions. The choice of the copula function as well as the latent hazard functions results in a flexible class of survival functions that is able to represent hazard rate functions with unusual shapes, such as bathtub or multimodal curves, while also modeling local effects associated with competing risks. The model is applied to two sets of simulated data as well as to data representing the unemployment duration of a sample of socially insured German workers. Model identification and estimation are also discussed.

Fusion and inference from multiple and massive disparate data sources—the requirement for our most challenging data analysis problems and the goal of our most ambitious statistical pattern recognition methodologies—has many and varied aspects which are currently the target of intense research and development. One aspect of the overall challenge is manifold matching—identifying embeddings of multiple disparate data spaces into the same low-dimensional space where joint inference can be pursued. We investigate this manifold matching task from the perspective of jointly optimizing the fidelity of the embeddings and their commensurability with one another, with a specific statistical inference exploitation task in mind. Our results demonstrate when and why our joint optimization methodology is superior to either version of separate optimization. The methodology is illustrated with simulations and an application in document matching.