Variance and covariance inequalities for truncated joint normal distribution via monotone likelihood ratio and log-concavity

JOURNAL OF MULTIVARIATE ANALYSIS

卷:139

Article

Mukerjee, Rahul¹  Ong, S. H.² 

[1] Indian Inst Management, Kolkata 700104, India

[2] Univ Malaya, Inst Math Sci, Kuala Lumpur 50603, Malaysia

关键词: Chi-square distribution;    Covariance matrix reconstruction;    Positive linear combination;    Stochastic ordering;   

DOI  :  10.1016/j.jmva.2015.02.010

来源: Elsevier

【 摘 要 】

Let X similar to N-v(0, Lambda) be a normal vector in v (>= 1) dimensions, where Lambda 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 Lambda 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free