an:02100226
Zbl 1218.62059
Shashkin, A. P.
Quasi-associatedness of a Gaussian system of random vectors
EN
Russ. Math. Surv. 57, No. 6, 1243-1244 (2002); translation from Usp. Mat. Nauk 57, No. 6, 199-200 (2002).
00095932
2002
j
62H20 62H05
From the paper: \textit{L.D. Pitt} [Ann. Probab. 10, 496--499 (1982; Zbl 0482.62046)] proved that a Gaussian system \(\{\xi_t, t \in T\}\) of real random variables is associated if and only if the covariances \(\text{cov}(\xi_s, \xi_t)\) are non-negative for all \(s, t \in T\). According to \textit{K. Joag-Dey} and \textit{F. Proschan} [Ann. Stat. 11, 286--295 (1983; Zbl 0508.62041)] negative associatedness of a Gaussian system is equivalent to the condition that \(\text{cov}(\xi_s, \xi_t)\leq 0\) for \(s\neq t\). The goal of this note is to prove that Gaussian systems of random vectors \(\{\xi_t, t \in T\}\) with values in \(\mathbb R^s\) are quasi-associated.
Zbl 0482.62046; Zbl 0508.62041