Exact exponential tail estimation for sums of independent centered random variables, under natural norming, with applications to the theory of U-statistics

2024/09/08 by M. R. Formica, Formica, M. R., E. Ostrovsky +3
Decision Sciences · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2409.05083

openalex publication_date 2024/09/08 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of Grand Lebesgue Spaces (GLS). We consider also some applications into the theory of U statistics, where we deduce alike for the independent variables the refined exponential tail estimates for ones under natural norming sequence.

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