Object orientation provides a flexible framework for the implementation of
the convolution of arbitrary distributions of real-valued random variables.

We discuss an algorithm which is based on the Discrete Fourier Transformation
and its fast computability via the Fast Fourier Transformation. It directly
applies to lattice-supported distributions. In the case of continuous
distributions an additional discretization to a linear lattice is necessary and
the resulting lattice-supported distributions are suitably smoothed after
convolution.

We provide an asymptotic expansion of the maximal mean squared error (MSE) of
the sample median to be attained on shrinking gross error neighborhoods about
an ideal central distribution. More specifically, this expansion comes in
powers of n^{-1/2}, for n the sample size, and uses a shrinking rate of
n^{-1/2} as well. This refines corresponding results of first order asymptotics
to be found in Rieder[94]. In contrast to usual higher order asymptotics, we do
not approximate distribution functions (or densities) in the first place, but
rather expand the risk directly.

We study global and local robustness properties of several estimators for
shape and scale in a generalized Pareto model. The estimators considered in
this paper cover maximum likelihood estimators, skipped maximum likelihood
estimators, Cram\'er-von-Mises Minimum Distance estimators, and, as a special
case of quantile-based estimators, Pickands Estimator. We further consider an
estimator matching the population median and an asymmetric, robust estimator of
scale (kMAD) to the empirical ones (kMedMAD), which may be tuned to an expected
FSBP of 34%.

We define Fisher information of scale of any distribution function F on the
real line by

I_{sca}(F):= sup (integral x phi'(x) F(dx))^2 / (integral phi^2(x) F(dx)),
phi in C_{c1}