Radhakrishna Rao, C.
(1969)
*A decomposition theorem for vector variables with a linear structure*
The Annals of Mathematical Statistics, 40
(5).
pp. 1845-1849.
ISSN 0003-4851

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Official URL: http://www.jstor.org/stable/2239575

## Abstract

A vector variable X is said to have a linear structure if it can be written as X=AY where A is a matrix and Y is a vector of independent random variables called structural variables. In earlier papers the conditions under which a vector random variable admits different structural representations have been studied. It is shown, among other results, that complete non-uniqueness, in some sense, of the linear structure characterizes a multivariate normal variable. In the present paper we prove a general decomposition theorem which states that any vector variable X with a linear structure can be expressed as the sum X_{1} + X_{2} of two independent vector variables X_{1}, X_{2} of which X_{1} is non-normal and has a unique linear structure, and X_{2} is multivariate normal variable with a nonunique linear structure.

Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Mathematical Statistics. |

ID Code: | 71499 |

Deposited On: | 25 Nov 2011 12:42 |

Last Modified: | 25 Nov 2011 12:42 |

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