  In many applications one is interested to detect certain (known) patterns in
the mean of a process with smallest delay. Using an asymptotic framework which
allows to capture that feature, we study a class of appropriate sequential
nonparametric kernel procedures under local nonparametric alternatives. We
prove a new theorem on the con- vergence of the normed delay of the associated
sequential detection procedure which holds for dependent time series under a
weak mixing condition. The result suggests a simple procedure to select a
kernel from a finite set of candidate kernels, and therefore may also be of
interest from a practical point of view. Further, we provide two new theorems
about the existence and an explicit representation of optimal kernels
minimizing the asymptotic normed delay. The results are illustrated by some
examples.
