On normal approximations to $U$-statistics

Vidmantas Bentkus, Bing-Yi Jing, Wang Zhou

Let $X_1,...,X_n$ be i.i.d. random observations. Let $\mathbb{S}=\mathbb{L}+\mathbb{T}$ be a $U$-statistic of order $k\ge 2$ where $\mathbb{L}$ is a linear statistic having asympt…