Order statistics from exchangeable random variables are always sufficient

05/16/2022

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by   Nickos Papadatos, et al.

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