Year: 2026
Type: preprint
Abstract: We prove that the classical Efron--Stein inequality holds for independent exchangeable pairs \((X_i,Y_i)\). The same inequality fails for independent identically distributed pairs; a simple trigonometric counterexample shows that the trivial Cauchy--Schwarz bound of factor \(n\) is sharp. When each random variable takes at most \(k_i\) values, a useful bound still holds with explicit constant \(ρ(k)\le\max_i k_i/2\).
Source: arXiv (Cornell University)
Authors: Baslingker, Jnaneshwar, Virág, Bálint
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160644384
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