The Asymptotic Distribution of Trimmed Sums
The Asymptotic Distribution of Trimmed Sums
Let $X_{1,n} \leq \cdots \leq X_{n,n}$ be the order statistics of $n$ independent and identically distributed random variables and let $m_n$ and $k_n$ be positive integers such that $m_n \rightarrow \infty, k_n \rightarrow \infty, m_n/n \rightarrow 0$ and $k_n/n \rightarrow 0$ as $n \rightarrow \infty$. We find a necessary and …