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 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.Comment: 14 pages, 13 figures. Submitted to IEEE Transactions on Information Theor

Eigen-Inference Moments Method for CognitiveWireless Communications

International audienceIn many situations, telecommunication engineers are faced with the problem of extracting information from the network. This corresponds in many cases to infer on functionals of spectrum of random matrices with only a limited knowledge on the statistics of the matrix entries. Here, the inference on the spectrum of random matrices is realized by moments method. In its full generality, the problem requires some sophisticated tools related to free probability theory and the explicit spectrum (complete information) can hardly be obtained (except for some trivial cases). Results in the asymptotic case and in the finite case are presented and simulations show how the moments method approach can be applied in practice. Several still open problems in this field are also presented

Signal Processing in Large Systems: a New Paradigm

For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to \infty$. Modern technological and societal advances now demand the study of sometimes extremely large populations and simultaneously require fast signal processing due to accelerated system dynamics. This results in not-so-large practical ratios $n/N$, sometimes even smaller than one. A disruptive change in classical signal processing methods has therefore been initiated in the past ten years, mostly spurred by the field of large dimensional random matrix theory. The early works in random matrix theory for signal processing applications are however scarce and highly technical. This tutorial provides an accessible methodological introduction to the modern tools of random matrix theory and to the signal processing methods derived from them, with an emphasis on simple illustrative examples

Finite Dimensional Statistical Inference

International audienceIn 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