2023/04/05 by Aaditya Ramdas, Ramdas, Aaditya, Tudor Manole +1 · 3 citations
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Methodology (stat.ME) #Probability (math.PR) #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2304.02611
openalex publication_date 2023/04/05 · openalex created_date 2023/04/07 · openalex updated_date 2026/07/28
We present simple randomized and exchangeable improvements of Markov's inequality, as well as Chebyshev's inequality and Chernoff bounds. Our variants are never worse and typically strictly more powerful than the original inequalities. The proofs are short and elementary, and can easily yield similarly randomized or exchangeable versions of a host of other inequalities that employ Markov's inequality as an intermediate step. We point out some simple statistical applications involving tests that combine dependent e-values. In particular, we uniformly improve the power of universal inference, and obtain tighter betting-based nonparametric confidence intervals. Simulations reveal nontrivial gains in power (and no losses) in a variety of settings.