Factor analysis with finite data

Valentina Ciccone; Augusto Ferrante; Mattia Zorzi

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arXiv · 1708.00401

Factor analysis with finite data

Valentina Ciccone·Augusto Ferrante·Mattia Zorzi

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Abstract

Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a diagonal matrix $D$ | accounting for the idiosyncratic noise in the data | and a low rank matrix $R$ | accounting for the variance of the common factors | in such a way that the rank of $R$ is as small as possible so that the number of common factors is minimal. In practice, however, the matrix $\Sigma$ is unknown and must be replaced by its estimate, i.e. the sample covariance, which comes from a finite amount of data. This paper provides a strategy to account for the uncertainty in the estimation of $\Sigma$ in the factor analysis problem.

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Valentina Ciccone, Augusto Ferrante, Mattia Zorzi. 2017-08-01. Factor analysis with finite data. https://arxiv.org/abs/1708.00401

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