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.

翻译：统计推断中高维数据的位置检验问题具有显著挑战性。现有文献提出了多种方法，其中许多对基础协方差矩阵施加了较强的正则性条件以确保检验统计量的渐近正态分布，这导致了检验水平控制的困难。为解决此问题，近期提出了一组采用正态参考方法的检验。此外，在R中通过C++实现的高维位置检验包的可选方案有限。本文介绍了利用正态参考方法检验具有潜在不同协方差矩阵的高维样本均值向量相等性的最新方法。我们提出了一个名为HDNRA的R包来展示这些检验的实现，其应用范围从两样本问题扩展至一般线性假设检验（GLHT）。该包提供了便捷、用户友好的检验访问接口，其核心使用Rcpp、OpenMP和RcppArmadillo通过C++实现，以确保高效执行。本文重新审视了这些正态参考检验的理论性质，并提供了基于真实数据集使用不同检验的示例。