Uniform estimates for order statistics and Orlicz functions

2008/09/17 by Y. Gordon, Yehoram Gordon, Gordon, Yehoram +8
Computer Science · Mathematics · #46B45 #46E40 #60B11 #60E15 #60G15 #62G30 #Bayesian Methods and Mixture Models #Distribution (mathematics) #Distribution function #Econometrics #Economics #FOS: Mathematics #Function (biology) #Independent and identically distributed random variables #Mathematical analysis #Mathematics #Order (exchange) #Order statistic #Physics #Probability (math.PR) #Random variable #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics #Statistics Theory (math.ST) #math.PR #math.ST #msc:46B45 #msc:46E40 #msc:60B11 #msc:60E15 #msc:60G15 #msc:62G30 #stat.TH

paper · pdf · doi:10.48550/arxiv.0809.2989

arxiv created 2008/09/17 · openalex publication_date 2008/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We establish uniform estimates for order statistics of sequences of independent identically distributed random variables with log-concave distribution in terms of Orlicz norms associated with the distribution function of the random variables.

Citations

• Gaussian averages of interpolated bodies and applications to approximate reconstruction

Related

• On the Distribution of the Expected Values of the Order Statistics
• Inequalities and bounds for expected order statistics from transform-ordered families
• Empirical Orlicz norms
• An Inversion Formula for Orlicz Norms and Sequences of Random Variables
• Order statistics on the spacings between order statistics for the uniform distribution