2020/10/16 by Jaehyeok Shin, Aaditya Ramdas, Shin, Jaehyeok +3
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.2010.08082
53 pages, 8 figures
arxiv created 2021/05/14 · arxiv updated 2021/05/17
We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for the mean of a univariate distribution. By utilizing a geometric interpretation of the GLR statistic, we derive a simple analytic upper bound on the probability that it exceeds any prespecified boundary; these are intractable to approximate via simulations due to infinite horizon of the tests and the composite nonparametric nulls under consideration. Using time-uniform boundary-crossing inequalities, we carry out a unified nonasymptotic analysis of expected sample sizes of one-sided and open-ended tests over nonparametric classes of distributions (including sub-Gaussian, sub-exponential, sub-gamma, and exponential families). Finally, we present a flexible and practical method to construct time-uniform confidence sequences that are easily tunable to be uniformly close to the pointwise Chernoff bound over any target time interval.