Nonparametric Iterated-Logarithm Extensions of the Sequential Generalized Likelihood Ratio Test

被引：1
作者：
Shin J. [1 ]
Ramdas A. [2 ]
Rinaldo A. [1 ]
机构：
[1] Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, 15213, PA
[2] Department of Statistics and Data Science and the Machine Learning Department, Carnegie Mellon University, Pittsburgh, 15213, PA
来源：
IEEE Journal on Selected Areas in Information Theory | 2021年 / 2卷 / 02期
关键词：
error probability; maximum likelihood detection; Sequential analysis; testing;
D O I：
10.1109/JSAIT.2021.3081105
中图分类号：
学科分类号：
摘要：
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. © 2020 IEEE.
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页码：691 / 704
页数：13
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