HDNRA - High-Dimensional Location Testing with Normal-Reference Approaches

Provides inverse-free high-dimensional location tests for two-sample and general linear hypothesis testing (GLHT) problems under equal or unequal covariance structures. The package implements classical normal-approximation procedures, scale-invariant procedures, normal-reference procedures based on covariance-matched Gaussian companions, and F-type normal-reference calibrations for heteroscedastic Behrens-Fisher and GLHT settings. Implemented two-sample normal-approximation and scale-invariant procedures include Bai and Saranadasa (1996) <https://www.jstor.org/stable/24306018>, Chen and Qin (2010) <doi:10.1214/09-aos716>, Srivastava and Du (2008) <doi:10.1016/j.jmva.2006.11.002>, and Srivastava et al. (2013) <doi:10.1016/j.jmva.2012.08.014>. Implemented two-sample normal-reference procedures include Zhang, Guo, Zhou and Cheng (2020) <doi:10.1080/01621459.2019.1604366>, Zhang, Zhou, Guo and Zhu (2021) <doi:10.1016/j.jspi.2020.11.008>, Zhang, Zhu and Zhang (2020) <doi:10.1016/j.ecosta.2019.12.002>, Zhang, Zhu and Zhang (2023) <doi:10.1080/02664763.2020.1834516>, Zhang and Zhu (2022) <doi:10.1080/10485252.2021.2015768>, Zhang and Zhu (2022) <doi:10.1007/s42519-021-00232-w>, and Zhu, Wang and Zhang (2023) <doi:10.1007/s00180-023-01433-6>. Implemented GLHT normal-approximation procedures include Fujikoshi et al. (2004) <doi:10.14490/jjss.34.19>, Srivastava and Fujikoshi (2006) <doi:10.1016/j.jmva.2005.08.010>, Yamada and Srivastava (2012) <doi:10.1080/03610926.2011.581786>, Schott (2007) <doi:10.1016/j.jmva.2006.11.007>, and Zhou, Guo and Zhang (2017) <doi:10.1016/j.jspi.2017.03.005>. Implemented GLHT normal-reference procedures include Zhang, Guo and Zhou (2017) <doi:10.1016/j.jmva.2017.01.002>, Zhang, Zhou and Guo (2022) <doi:10.1016/j.jmva.2021.104816>, Zhu, Zhang and Zhang (2022) <doi:10.5705/ss.202020.0362>, Zhu and Zhang (2022) <doi:10.1007/s00180-021-01110-6>, Zhang and Zhu (2022) <doi:10.1016/j.csda.2021.107385>, and Cao et al. (2024) <doi:10.1007/s00362-024-01530-8>. The package also includes the random-integration normal-approximation GLHT procedure of Li et al. (2025) <doi:10.1007/s00362-024-01624-3>. A package-level overview is given in Wang, Zhu and Zhang (2026) <doi:10.1016/j.csda.2025.108269>.