This article is cited in 12 papers

Short Communications

On the estimation of moments of sums of independent random variables

V. V. Sazonov

Moscow

Abstract: Let $\mathscr G$ be the class of real valued functions satisfying conditions (1). It is proved that if $\xi_1,\dots,\xi_n$ are independent random variables such that $\mathbf E\xi_i=0$ and $\mathbf E|\xi_i|^mg(\xi_i)<\infty$ for some integer $m\ge2$ and some $g\in\mathscr G$, $g(\,\cdot\,)\ne|\,\cdot\,|^\delta$, $0\le\delta\le1$, then the inequality (2) holds true; in the case $g(\,\cdot\,)=|\,\cdot\,|^\delta$ a slightly better inequality is proved.

Received: 13.07.1973

 English version: Theory of Probability and its Applications, 1975, 19:2, 371–374

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