Spacings (that is, the differences between successive order statistics) are useful in various applications in statistics. Many properties of the spacing are known when the spacings are constructed ...

Let $X_1, X_2, \cdots$ be a sequence of i.i.d. random vectors taking values in a space $V$, let $\bar{X}_n = (X_1 + \cdots + X_n)/n$, and for $J \subset V$ let $a_n(J ...