  Langevin models are frequently used to model various stochastic processes in
different fields of natural and social sciences. They are adapted to measured
data by estimation techniques such as maximum likelihood estimation, Markov
chain Monte Carlo methods, or the non-parametric direct estimation method
introduced by Friedrich et al. The latter has the distinction of being very
effective in the context of large data sets. Due to their $\delta$-correlated
noise, standard Langevin models are limited to Markovian dynamics. A
non-Markovian Langevin model can be formulated by introducing a hidden
component that realizes correlated noise. For the estimation of such a
partially observed diffusion a different version of the direct estimation
method was introduced by Lehle et al. However, this procedure includes the
limitation that the correlation length of the noise component is small compared
to that of the measured component. In this work we propose another version of
the direct estimation method that does not include this restriction. Via this
method it is possible to deal with large data sets of a wider range of examples
in an effective way. We discuss the abilities of the proposed procedure using
several synthetic examples.
