Asymptotic Distribution of Symmetric Statistics
对称统计量的渐近分布
Sequences of $m$th order symmetric statistics are examined for convergence in law. Under appropriate conditions, a limiting distribution exists and is equivalent to that of a linear combination of products of Hermite polynomials of independent $N(0, 1)$ random variables. Connections with the work of von Mises, Hoeffding, and Filippova are noted.