HDNRA: An R package for HDLSS location testing with normal-reference approaches

TL;DR

This paper introduces HDNRA, an R package implementing normal-reference tests for high-dimensional location testing, addressing size control issues and extending to general linear hypotheses with efficient C++ implementation.

Contribution

The paper presents a new R package, HDNRA, that implements recent normal-reference tests for high-dimensional mean vector equality, including general linear hypotheses, with efficient C++ code.

Findings

The package enables easy application of high-dimensional location tests in R.

The tests maintain size control under various conditions.

Examples demonstrate practical use on real datasets.

Abstract

The challenge of location testing for high-dimensional data in statistical inference is notable. Existing literature suggests various methods, many of which impose strong regularity conditions on underlying covariance matrices to ensure asymptotic normal distribution of test statistics, leading to difficulties in size control. To address this, a recent set of tests employing the normal-reference approach has been proposed. Moreover, the availability of tests for high-dimensional location testing in R packages implemented in C++ is limited. This paper introduces the latest methods utilizing normal-reference approaches to test the equality of mean vectors in high-dimensional samples with potentially different covariance matrices. We present an R package named HDNRA to illustrate the implementation of these tests, extending beyond the two-sample problem to encompass general linear hypothesis testing (GLHT). The package offers easy and user-friendly access to these tests, with its core implemented in C++ using Rcpp, OpenMP and RcppArmadillo for efficient execution. Theoretical properties of these normal-reference tests are revisited, and examples based on real datasets using different tests are provided.