Finite Dimensional Statistical Inference

Details Finite Dimensional Statistical Inference Finite Dimensional Statistical Inference

2009-11-29

arxiv.org/abs/0911.5515v2

Computer Science

Information Theory

14 pages, 13 figures. Submitted to IEEE Transactions on Information Theory

Scientific paper

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 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.

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