  Compared to widely used likelihood-based approaches, the minimum contrast
(MC) method offers a computationally efficient method for estimation and
inference of spatial point processes. These relative gains in computing time
become more pronounced when analyzing complicated multivariate point process
models. Despite this, there has been little exploration of the MC method for
multivariate spatial point processes. Therefore, this article introduces a new
MC method for parametric multivariate spatial point processes. A contrast
function is computed based on the trace of the power of the difference between
the conjectured $K$-function matrix and its nonparametric unbiased
edge-corrected estimator. Under standard assumptions, we derive the asymptotic
normality of our MC estimator. The performance of the proposed method is
demonstrated through simulation studies of bivariate log-Gaussian Cox processes
and five-variate product-shot-noise Cox processes.
