Macquarie Seminar on Stochastic Finance : Prof. Reiss -- Using Covariate Information in Extreme Value Models

At the beginning we recall basic facts about the well-known linear
regression
problem in a fixed and a random design. It is indicated that the
random
design problem conditioned on the independent variate (the covariate)
can
be regarded as a fixed design problem. Afterwards the considerations
are
merely based on the conditional statistical model. In contrary to the
foregoing
models we deal with parametric models such as the EV model. Based
on a conditional maximum likelihood estimator one obtains estimators
and
predictions of conditional functional parameters. The required
modifications
for gP distributions are deduced within a Poisson process framework.
Applications in environmental statistics and statistical finance are
indicated.