Order statistics from exchangeable random variables are always sufficient

Abstract

Let $(X_1,\dots ,X_n)$ be an exchangeable random vector with distribution function $F$, and denote by $Y_1\le \cdots \le Y_n$ the corresponding order statistics. We show that the conditional distribution of $(X_1,\dots ,X_n)$ given $(Y_1,\dots ,Y_n)$ does not depend on $F$.

2 pages