  We estimate the rate of convergence for the Kantorovich (or Wasserstein)
distance between empirical measures of i.i.d. random variables associated with
the Laguerre model of order $\alpha$ on $(0,\infty)^N$ and their common law,
which is not compactly supported and has no rotational symmetry. Compared with
the Gaussian case, our result is sharp provided the parameter $\alpha$ and the
dimension $N$ are chosen in a specified regime.
