  Estimating function inference is indispensable for many common point process
models where the joint intensities are tractable while the likelihood function
is not. In this paper we establish asymptotic normality of estimating function
estimators in a very general setting of non-stationary point processes. We then
adapt this result to the case of non-stationary determinantal point processes
which are an important class of models for repulsive point patterns. In
practice often first and second order estimating functions are used. For the
latter it is common practice to omit contributions for pairs of points
separated by a distance larger than some truncation distance which is usually
specified in an ad hoc manner. We suggest instead a data-driven approach where
the truncation distance is adapted automatically to the point process being
fitted and where the approach integrates seamlessly with our asymptotic
framework. The good performance of the adaptive approach is illustrated via
simulation studies for non-stationary determinantal point processes and by an
application to a real dataset.
