Please Note: This seminar will be given online.
|
Statistics & Biostatistics seminar series
Harry
Joe Link to join seminar: Hosted on Zoom |
Estimation of copula-based tail quantities
Let
$F$
be
a
$d$-dimensional
distribution,
say
of
risk
variables.
With
a
random
sample
from
$F$.
Under
weak
assumptions
on
the
form
of
the
tail
of
the
copula
$C$
of
$F$,
based
on
a
random
sample
from
$F$,
we
estimate
quantities
such
as
(a)
extreme
joint
tail
probabilities,
(b)
multivariate
return
curves/surfaces,
(c)
tail
dependence
parameters,
(d)
tail
order,
(e)
tail-weighted
dependence
measures.
The
main
theory
is
based
on
(i)
tail
expansions
of
the
distribution
$D()$
of
directional
maxima
or
minima
of
random
vectors
in
the
copula
scale
and
(ii)
tail
expansions
of
an
integral
of
$D()$.
Item
(ii)
comes
from
investigating
a
tail-weighted
dependence
measure
that
arises
from
estimating
the
extremal
index
for
multivariate
extreme
value
data.
The
estimation
methods
for
extreme
joint
tail
probabilities
consist
of
likelihood-based
threshold
methods
(for
observations
of
appropriate
maxima/minima
that
lie
beyond
a
threshold).
Examples
will
be
used
for
illustration
of
the
main
ideas.