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Numerical Reconstruction of the Covariance Matrix of a Spherically Truncated Multinormal Distribution
Joint Authors
Palombi, Filippo
Toti, Simona
Filippini, Romina
Source
Journal of Probability and Statistics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-01-10
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
We relate the matrix SB of the second moments of a spherically truncated normal multivariate to its full covariance matrix Σ and present an algorithm to invert the relation and reconstruct Σ from SB.
While the eigenvectors of Σ are left invariant by the truncation, its eigenvalues are nonuniformly damped.
We show that the eigenvalues of Σ can be reconstructed from their truncated counterparts via a fixed point iteration, whose convergence we prove analytically.
The procedure requires the computation of multidimensional Gaussian integrals over an Euclidean ball, for which we extend a numerical technique, originally proposed by Ruben in 1962, based on a series expansion in chi-square distributions.
In order to study the feasibility of our approach, we examine the convergence rate of some iterative schemes on suitably chosen ensembles of Wishart matrices.
We finally discuss the practical difficulties arising in sample space and outline a regularization of the problem based on perturbation theory.
American Psychological Association (APA)
Palombi, Filippo& Toti, Simona& Filippini, Romina. 2017. Numerical Reconstruction of the Covariance Matrix of a Spherically Truncated Multinormal Distribution. Journal of Probability and Statistics،Vol. 2017, no. 2017, pp.1-24.
https://search.emarefa.net/detail/BIM-1186284
Modern Language Association (MLA)
Palombi, Filippo…[et al.]. Numerical Reconstruction of the Covariance Matrix of a Spherically Truncated Multinormal Distribution. Journal of Probability and Statistics No. 2017 (2017), pp.1-24.
https://search.emarefa.net/detail/BIM-1186284
American Medical Association (AMA)
Palombi, Filippo& Toti, Simona& Filippini, Romina. Numerical Reconstruction of the Covariance Matrix of a Spherically Truncated Multinormal Distribution. Journal of Probability and Statistics. 2017. Vol. 2017, no. 2017, pp.1-24.
https://search.emarefa.net/detail/BIM-1186284
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186284