Nonparametric iterated-logarithm extensions of the sequential generalized likelihood ratio test

10/16/2020
by   Jaehyeok Shin, et al.
0

We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding confidence sequences. By utilizing a geometrical interpretation of the GLR statistic, we present a simple upper bound on the probability that it exceeds any prespecified boundary function. Using time-uniform boundary-crossing inequalities, we carry out a nonasymptotic analysis of the sample complexity of one-sided and open-ended tests over nonparametric classes of distributions, including sub-Gaussian, sub-exponential, and exponential family distributions in a unified way. We propose a flexible and practical method to construct confidence sequences for the corresponding problem that are easily tunable to be uniformly close to the pointwise Chernoff bound over any target time interval.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/18/2018

Uniform, nonparametric, non-asymptotic confidence sequences

A confidence sequence is a sequence of confidence intervals that is unif...
research
12/24/2019

Universal Inference Using the Split Likelihood Ratio Test

We propose a general method for constructing hypothesis tests and confid...
research
11/28/2018

Mixture Martingales Revisited with Applications to Sequential Tests and Confidence Intervals

This paper presents new deviation inequalities that are valid uniformly ...
research
11/23/2022

Nonparametric Likelihood Ratio Test for Univariate Shape-constrained Densities

We provide a comprehensive study of a nonparametric likelihood ratio tes...
research
03/16/2021

Sequential Estimation of Convex Divergences using Reverse Submartingales and Exchangeable Filtrations

We present a unified technique for sequential estimation of convex diver...
research
12/29/2022

Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations

Sequential testing, always-valid p-values, and confidence sequences prom...
research
03/19/2020

Chernoff-type Concentration of Empirical Probabilities in Relative Entropy

We study the relative entropy of the empirical probability vector with r...

Please sign up or login with your details

Forgot password? Click here to reset