  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, this expression 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.
The performances of the associated estimator 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.
