LqRT: Robust Hypothesis Testing of Location Parameters using Lq-Likelihood-Ratio-Type Test in Python

11/27/2019
by   Anton Alyakin, et al.
0

A t-test is considered a standard procedure for inference on population means and is widely used in scientific discovery. However, as a special case of a likelihood-ratio test, t-test often shows drastic performance degradation due to the deviations from its hard-to-verify distributional assumptions. Alternatively, in this article, we propose a new two-sample Lq-likelihood-ratio-type test (LqRT) along with an easy-to-use Python package for implementation. LqRT preserves high power when the distributional assumption is violated, and maintains the satisfactory performance when the assumption is valid. As numerical studies suggest, LqRT dominates many other robust tests in power, such as Wilcoxon test and sign test, while maintaining a valid size. To the extent that the robustness of the Wilcoxon test (minimum asymptotic relative efficiency (ARE) of the Wilcoxon test vs the t-test is 0.864) suggests that the Wilcoxon test should be the default test of choice (rather than "use Wilcoxon if there is evidence of non-normality", the default position should be "use Wilcoxon unless there is good reason to believe the normality assumption"), the results in this article suggest that the LqRT is potentially the new default go-to test for practitioners.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

04/29/2021

Gaussian Universal Likelihood Ratio Testing

The likelihood ratio test (LRT) based on the asymptotic chi-squared dist...
12/07/2018

A tutorial on generalizing the default Bayesian t-test via posterior sampling and encompassing priors

With the advent of so-called default Bayesian hypothesis tests, scientis...
08/03/2020

A Robust Spearman Correlation Coefficient Permutation Test

In this work, we show that Spearman's correlation coefficient test about...
05/08/2018

Seeking evidence of absence: Reconsidering tests of model assumptions

Statistical tests can only reject the null hypothesis, never prove it. H...
01/12/2020

Error Exponents of Mismatched Likelihood Ratio Testing

We study the problem of mismatched likelihood ratio test. We analyze the...
11/11/2019

A post hoc test on the Sharpe ratio

We describe a post hoc test for the Sharpe ratio, analogous to Tukey's t...
06/20/2021

Combined tests based on restricted mean time lost for competing risks data

Competing risks data are common in medical studies, and the sub-distribu...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.