A lower confidence sequence for the changing mean of non-negative right heavy-tailed observations with bounded mean

• URL: http://arxiv.org/abs/2210.11133v1
• Date: Thu, 20 Oct 2022 09:50:05 GMT
• Title: A lower confidence sequence for the changing mean of non-negative right heavy-tailed observations with bounded mean
• Authors: Paul Mineiro
• Abstract summary: A confidence sequence produces an adapted sequence of sets for a predictable parameter sequence with a time-parametric coverage guarantee. This work constructs a non-asymptotic lower CS for the running average conditional expectation whose slack converges to zero.
• Score: 9.289846887298854
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 unknown $(1 + \delta)$-th moment bound; and can be efficiently approximated using a sublinear number of sufficient statistics. In certain cases this lower CS can be converted into a closed-interval CS whose width converges to zero, e.g., any bounded realization, or post contextual-bandit inference with bounded rewards and unbounded importance weights. A reference implementation and example simulations demonstrate the technique.

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