Probability Bounds, Multivariate Normal Distribution and an Integro-Differential Inequality for Random Vectors

B. L. S. Prakasa Rao
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B. L. S. Prakasa Rao: Delhi Centre, Indian Statistical Institute

A chapter in Stochastic Processes, 1993, pp 275-284 from Springer

Abstract: Abstract In the light of an inequality derived by Chernoff (1981), a characterization of the normal distribution was obtained by Borovkov and Utev (1983). Prakasa Rao and Sreehari (1986) derived a multivariate analogue characterizing the multivariate normal distribution. A bound is obtained for the variation between the probability distribution of a random vector with mean zero and a finite covariance matrix Σ and the corresponding multivariate normal distribution with mean zero and the same covariance matrix Σ. As applications, characterization of a multivariate normal distribution due to Prakasa Rao and Sreehari (1986) is derived and a multivariate limit theorem is given. Results obtained extend the work of Utev (1989). Inter alia, an integro-differential inequality valid for random vectors with finite covariance matrix is obtained.

Keywords: Covariance Matrix; Random Vector; Differentiable Function; Borel Subset; Multivariate Normal Distribution (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-7909-0_30

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DOI: 10.1007/978-1-4615-7909-0_30

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