Finite-Sample Tail Bound of Likelihood Ratio Test under Multinomial Sampling

Computes a finite-sample tail bound for the log-likelihood ratio test (LRT) statistic under multinomial sampling. The resulting bound is used to compute finite-sample conservative p-values and critical values when the standard chi-squared asymptotics can be unreliable. The package also supports multiple independent multinomial trials.

multChernoff

This package computes a finite-sample tail bound of the likelihood ratio test (LRT) under multinomial sampling. The tail bounds can be used to obtain conservative p-values and critical values. This is useful for inference when the sample size is comparable to or even smaller than the alphabet size, where the standard chi-square asymptotic (Wilks' theorem) may not hold.

Installation

You can install the package from CRAN with

> install.packages("multChernoff")

or from GitHub with

> devtools::install_github("richardkwo/multChernoff")

Usage

Please refer to the vignette.

> vignette("multChernoff")

The package can be used with the finite-sample critical value criticalValue to construct a convex confidence region on the underlying probability vector.

Reference

The method is based on the following work:

F. Richard Guo and Thomas S. Richardson, "Chernoff-Type Concentration of Empirical Probabilities in Relative Entropy," in IEEE Transactions on Information Theory, vol. 67, no. 1, pp. 549-558, Jan. 2021.