Perform the Adaptable Regularized Hotelling's T2 test (ARHT) proposed by Li et al. (2016). Both one- and two- sample mean test are available with various probabilistic alternative prior models. It contains a function to consistently estimate higher order moments of the population covariance spectral distribution using the spectral of the sample covariance matrix. In addition, it contains a function to sample from 3-variate chi-squared random vectors approximately with a given correlation matrix when the degrees of freedom are large.
You can install ARHT from github with:
# install.packages("devtools") devtools::install_github("HaoranLi/ARHT")
This is a basic example which shows you how to solve a common problem:
library(ARHT) ## basic example code set.seed(10086) # One-sample test n1 = 300; p =500 dataX = matrix(rnorm(n1 * p), nrow = n1, ncol = p) res1 = ARHT(dataX) # Two-sample test n2= 400 dataY = matrix(rnorm(n2 * p), nrow = n2, ncol = p ) res2 = ARHT(dataX, dataY, mu_0 = rep(0.01,p)) # Specify probabilistic alternative priors model res3 = ARHT(dataX, dataY, mu_0 = rep(0.01,p), prob_alt_prior = list(c(1/3, 1/3, 1/3), c(0,1,0))) # Change Type 1 error calibration method res4 = ARHT(dataX, dataY, mu_0 = rep(0.01,p), Type1error_calib = "sqrt") RejectOrNot = res4$ARHT_pvalue < 0.05
Li, Haoran, Alexander Aue, Debashis Paul, Jie Peng, and Pei Wang. 2016. “An Adaptable Generalization of Hotelling's T2 Test in High Dimension.” arXiv preprint arXiv:1609.08725.
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