In this paper we propose a perturbative method for the reconstruction of the covariance matrix of a multinormal distribution, under the assumption that the only available information amounts to the covariance matrix of a spherically truncated counterpart of the same distribution. We expand the relevant equations up to the fourth perturbative order and discuss the analytic properties of the first few perturbative terms. We finally compare the proposed approach with an exact iterative algorithm (discussed in Palombi et al. (2017)) in the hypothesis that the spherically truncated covariance matrix is estimated from samples of various sizes.

A perturbative approach to the reconstruction of the eigenvalue spectrum of a normal covariance matrix from a spherically truncated counterpart

Palombi F.;
2020

Abstract

In this paper we propose a perturbative method for the reconstruction of the covariance matrix of a multinormal distribution, under the assumption that the only available information amounts to the covariance matrix of a spherically truncated counterpart of the same distribution. We expand the relevant equations up to the fourth perturbative order and discuss the analytic properties of the first few perturbative terms. We finally compare the proposed approach with an exact iterative algorithm (discussed in Palombi et al. (2017)) in the hypothesis that the spherically truncated covariance matrix is estimated from samples of various sizes.
Covariance reconstruction; Ill-posed problems; Perturbation theory; Regularization
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12079/53110
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