Optimal constants in the Rosenthal inequality for random variables with zero odd moments

被引：5
|
作者：
Ibragimov, Marat [2 ]
Ibragimov, Rustam [1 ]
机构：
[1] Harvard Univ, Dept Econ, Littauer Ctr, Cambridge, MA 02138 USA
[2] Tashkent State Econ Univ, Dept Probabil Theory, Tashkent, Uzbekistan
来源：
STATISTICS & PROBABILITY LETTERS | 2008年 / 78卷 / 02期
关键词：
Rosenthal inequality; moment inequalities; best constants;
D O I：
10.1016/j.spl.2007.05.018
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We obtain estimates for the best constant in the Rosenthal inequality E vertical bar Sigma(n)(i=1)xi(i)vertical bar(2m) <= C(2m) max(Sigma(n)(i=1) E xi(2m)(i), (Sigma(n)(i=1) E xi(2)(i))(m)) for independent random variables xi(1),...,xi(n) with l zero first odd moments, l >= 1. The estimates are sharp in the extremal cases l = 1 and l = m, that is, in the cases of random variables with zero mean and random variables with m zero first odd moments. (c) 2007 Elsevier B.V. All fights reserved.
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页码：186 / 189
页数：4
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