Asymptotic Analysis for U-Statistics and Its Application to Von Mises Statistics

• 作者: Timur Zubayraev
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: U-STATISTICS Von MISES STATISTICS SYMMETRIC STATISTICS
• 年，卷（期）: 2011,（3）
• 页码范围: 139-144
• 页数: 6页
• 分类号: O1

摘要

Let - be i.i.d. random variables taking values in a measurable space ( Χ, B ). Let φ1: Χ →□ and φ: Χ2→□ be measurable functions. Assume that φ is symmetric, i.e. φ(x,y)=φ(y.x), for any x,y∈Χ . Consider U-statistic, assuming that Eφ1(Χ)=0, Eφ(x, X)=0 for all x∈X, Eφ2(x,X)<∞, Eφ21(X)<∞. We will provide bounds for ΔN=supx|F(x)-F0(x)-F1(x)|, where F is a distribution function of T and F0 , F1 are its limiting distribution function and Edgeworth correction respectively. Applications of these results are also provided for von Mises statistics case.