This article is cited in 2 papers

Short Communications

On the characterization of multidimensional normal law by the independence of linear statistics

A. A. Zinger

Leningrad

Abstract: Let $\{X_j\}$ be a sequence of independent random vectors in $R^k$ and $\{A_j,B_j\}$ be a sequence of pairs of nonsingular real $(k\times k)$-matrices. It is shown that every $X_j$ has $k$-dimensional normal distribution if linear statistics (1) converge with probability 1 to independent random vectors and the condition (2) is satisfied.

Received: 29.09.1977

 English version: Theory of Probability and its Applications, 1979, 24:2, 388–392

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