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Title: Variance and covariance inequalities for truncated joint normal distribution via monotone likelihood ratio and log-concavity
Authors: Mukerjee, Rahul
Ong, Siewhui
Keywords: Chi-square distribution
Covariance matrix reconstruction
Positive linear combination
Stochastic ordering
Issue Date: 2015
Publisher: SCOPUS
Journal of Multivariate Analysis
Academic Press Inc.
Series/Report no.: 139
Abstract: Let X~Nv(0,?) be a normal vector in v(?1) dimensions, where ? is diagonal. With reference to the truncated distribution of X on the interior of a v-dimensional Euclidean ball, we completely prove a variance inequality and a covariance inequality that were recently discussed by Palombi and Toti (2013). These inequalities ensure the convergence of an algorithm for the reconstruction of ? only on the basis of the covariance matrix of X truncated to the Euclidean ball. The concept of monotone likelihood ratio is useful in our proofs. Moreover, we also prove and utilize the fact that the cumulative distribution function of any positive linear combination of independent chi-square variates is log-concave, even though the same may not be true for the corresponding density function. � 2015 Elsevier Inc.
Description: Mukerjee, Rahul, Indian Institute of Management Calcutta, Joka, Diamond Harbour Road, Kolkata, 700 104, India; Ong, Siewhui, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, 50603, Malaysia
ISSN/ISBN - 0047259X
DOI - 10.1016/j.jmva.2015.02.010
Appears in Collections:Operations Management

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