  Continuous determinantal point processes (DPPs) are a class of repulsive
point processes on $\mathbb{R}^d$ with many statistical applications. Although
an explicit expression of their density is known, it is too complicated to be
used directly for maximum likelihood estimation. In the stationary case, an
approximation using Fourier series has been suggested, but it is limited to
rectangular observation windows and no theoretical results support it. In this
contribution, we investigate a different way to approximate the likelihood by
looking at its asymptotic behaviour when the observation window grows towards
$\mathbb{R}^d$. This new approximation is not limited to rectangular windows,
is faster to compute than the previous one, does not require any tuning
parameter, and some theoretical justifications are provided. It moreover
provides an explicit formula for estimating the asymptotic variance of the
associated estimator. The performances are assessed in a simulation study on
standard parametric models on $\mathbb{R}^d$ and compare favourably to common
alternative estimation methods for continuous DPPs.
