Multivariate Dispersion Models

Dispersion Models for Extremes

We propose extreme value analogues of natural exponential families and exponential dispersionmodels and introduce the hazard slope as an analogue of the variance function. The set of quadraticand power hazard slopes is characterized, and is shown to include well-known distributions such asthe Rayleigh, Gumbel, power, Pareto, logistic, negative exponential, Weibull and Fréchet famili...

Multivariate Volatility Models

Multivariate volatility models are widely used in finance to capture both volatility clustering and contemporaneous correlation of asset return vectors. Here, we focus onmultivariate GARCHmodels. In this commonmodel class, it is assumed that the covariance of the error distribution follows a time dependent process conditional on information which is generated by the history of the process. To p...

Multivariate Spatial Process Models

Semiparametric Multivariate Garch Models

Estimation of multivariate GARCH models is usually carried out by quasi maximum likelihood (QMLE), for which recently consistency and asymptotic normality have been proven under quite general conditions. However, there are to date no results on the efficiency loss of QMLE if the true innovation distribution is not multinormal. We investigate this issue by suggesting a nonparametric estimation o...

Multivariate Linear Models

For example, we may have (i) measurements of d = 5 air pollutants (CO, NO, etc.) on n = 42 widely-separated days, (ii) d test scores for n different students, (iii) best results for d Olympic events for teams from n different countries, or (iv) d different physical measurements for n individuals (human or animal) that we are trying to classify. In each case, the i row corresponds to the i multi...