ABSTRACT
This chapter mainly emphasizes likelihood-based inference methods for estimation in parametric models and the use of diagnostics as a guide to choosing models and assessing their fits. Dependence models based on copulas are generally approximations and some results are stated with this point of view. Parametric families that can be easily constructed tend to have the property of monotone positive (or negative) dependence for bivariate margins. When bivariate margins do not have simple relationships then non-simple parametric families or non-parametric approaches can be considered; there is some discussion of the latter in Section 5.10.3.
