Finite dimensional statistical inference

In this paper, we derive the explicit series expansion of the eigenvalue distribution of various models, namely the case of non-central Wishart distributions as well as one sided correlated zero mean Wishart distributions. The tools used are borrowed from the free probability framework which have been quite successful for high dimensional statistical inference (when the size of the matrices tends to infinity), also known as free deconvolution. This contribution focuses on the finite Gaussian case and proposes algorithmic methods to compute the moments.