Finite Dimensional Statistical Inference

Øyvind Ryan (1) , Antonia Masucci (2) , Sheng Yang (3) , Merouane Debbah (2)

1 UiO - University of Oslo
2 Chaire Radio Flexible - Chaire Radio Flexible Alcatel-Lucent/Supélec
3 E3S - Supélec Sciences des Systèmes

In this paper, we derive the explicit series expansion of the eigenvalue distribution of various models, namely the case of noncentral Wishart distributions, as well as correlated zero mean Wishart distributions. The tools used extend those of 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. Cases where asymptotic results fail to apply are also discussed.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Øyvind Ryan, Antonia Masucci, Sheng Yang, Merouane Debbah. Finite Dimensional Statistical Inference. IEEE Transactions on Information Theory, 2011, 57 (4), pp.2457-2473. ⟨10.1109/TIT.2011.2112010⟩. ⟨hal-00632418⟩