2022/05/10 by Martina Cardone, Cardone, Martina, Alex Dytso +3
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (stat.ML) #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2205.04621
openalex publication_date 2022/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that ensures a stronger mode of convergence using the relative entropy. In particular, an order O(1/√(n)) rate of convergence is established under mild conditions on the parent distribution of the sample generating the order statistics. To prove this result, ancillary results on order statistics are derived, which might be of independent interest.