关于U统计量的一点注记

A Note on U Statistics

中文摘要:

      

英文摘要:

      Let φ(x₁,x₂,…x_m) be a real Borel measurable symmetrical function of the m variables, and let U_n denote the U-statistic with kernel φ. In this note it is proved that the necessary and sufficient condition for E|φ|< ∞ is that there exists an n≥m such that E|U_n|< ∞.