A lower confidence sequence for the changing mean of non-negative right heavy-tailed observations with bounded mean. (arXiv:2210.11133v1 [stat.ML])

A confidence sequence (CS) is an anytime-valid sequential inference primitive
which produces an adapted sequence of sets for a predictable parameter sequence
with a time-uniform coverage guarantee. This work constructs a non-parametric
non-asymptotic lower CS for the running average conditional expectation whose
slack converges to zero given non-negative right heavy-tailed observations with
bounded mean. Specifically, when the variance is finite the approach dominates
the empirical Bernstein supermartingale of Howard et. al.; with infinite
variance, can adapt to a known or …

arxiv confidence mean negative