One main theme of my research is dependence modelling, in which the multivariate responses can be binary, categorical, extreme value, heavy-tailed, etc. Non-normal time series can be considered as a special case, in which dependence is decreasing with lag. The theory is quite different from classical multivariate statistics.

The research problems here are challenging, as one must deal with existence of models with some desirable properties. For example, in extreme value inference, the concept of tail dependence of multivariate models must be considered. This area of research requires the study of methods for constructing parametric families and the search for new stochastic constructions and representations for models.

Inferential techniques have been developed so that the models are computationally feasible to work with. Inference methods based on low-dimensional margins have been studied; examples are two-stage estimation (or inference functions for margins) and composite likelihood.

Specific situations where I have made use of modern multivariate concepts include:

• extreme value inference for multivariate maxima,
• models for repeated measures or multivariate discrete (binary, ordinal, count) response in biostatistical applications
• time series models for non-normal response with covariates,
• models for familial data, in which families have different sizes and different pedigree structure,
• psychometrics models for item response data.

Current and future research includes development of models and inference procedures for multivariate applications in biostatistics, econometrics and finance, genetics, psychometrics and data mining.