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SUMMARY:Randomized and exchangeable improvements of Markov's\, Chebyshev's
  and Chernoff's inequalities - Aaditya Ramdas (Carnegie Mellon University)
DTSTART:20230526T130000Z
DTEND:20230526T140000Z
UID:TALK199492@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:We present simple randomized and exchangeable improvements of 
 Markov's inequality\, as well as the related Chebyshev's and Chernoff's in
 equalities (like Hoeffding's and Bernstein's)\, for example. Our variants 
 are never worse and typically strictly more powerful than the original ine
 qualities\, which can be recovered as simple corollaries. The proofs are s
 hort and somewhat elementary. We provide several simple statistical applic
 ations involving e-values\, such as uniformly improving the power of unive
 rsal inference\, and tighter nonparametric confidence intervals based on b
 etting.\n\nThis is joint work with Tudor Manole\, a PhD student at CMU. A 
 preprint is at https://arxiv.org/abs/2304.02611. 
LOCATION:MR12\, Centre for Mathematical Sciences
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