  We introduce a new method to qualify the goodness of fit parameter estimation
of compound Wishart models. Our method based on the free deterministic
equivalent Z-score, which we introduce in this paper. Furthermore, an
application to two dimensional autoregressive moving-average model is provided.
  Our proposal method is a generalization of statistical hypothesis testing to
one dimensional moving average model based on fluctuations of real compound
Wishart matrices, which is a recent result by Hasegawa, Sakuma and Yoshida.
