Order statistics from exchangeable random variables are always sufficient

2022/05/16 by Nickos Papadatos, Papadatos, Nickos
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Primary 62B05 #Probability (math.PR) #Probability and Risk Models #Secondary 62G30 #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2206.00044

openalex publication_date 2022/05/16 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

Let (X₁,…,X_n) be an exchangeable random vector with distribution function F, and denote by Y₁≤ ⋯≤ Y_n the corresponding order statistics. We show that the conditional distribution of (X₁,…,X_n) given (Y₁,…,Y_n) does not depend on F.

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