  The maximum composite likelihood estimator for parametric models of
determinantal point processes (DPPs) is discussed. Since the joint intensities
of these point processes are given by determinant of positive definite kernels,
we have the explicit form of the joint intensities for every order. This fact
enables us to consider the generalized maximum composite likelihood estimator
for any order. This paper introduces the two step generalized composite
likelihood estimator and shows the moment convergence of the estimator under a
stationarity. Moreover, our results can yield information criteria for
statistical model selection within DPPs.
