moments_PSD: Consistent estimators of high-order moments of the population...
In ARHT: Adaptable Regularized Hotelling's T^2 Test for High-Dimensional Data

Description Usage Arguments Value References Examples

The function calculates consistent estimators of moments of the spectral distribution of the population covariance matrix given the spectral of the sample covariance matrix.

1	moments_PSD(eigenvalues, n, mom_degree)

`eigenvalues`	all eigenvalues of the sample covariance matrix including 0's.
`n`	degree of freedom of the sample covariance matrix.
`mom_degree`	the maximum order of moments.

Estimators of moments from the first to the mom_degree -th order.

Bai, Z., Chen, J., & Yao, J. (2010). On estimation of the population spectral distribution from a high-dimensional sample covariance matrix. Australian & New Zealand Journal of Statistics, 52(4), 423-437.

set.seed(10086)
n = 400; p= 500
pop_eig = seq(10,1,length = p)
# Data with covariance matrix diag(pop_eig)
Z = matrix(rnorm(n*p),n,p)
X = Z %*% diag(sqrt(pop_eig))
raw_eig = svd(cov(X))$d
emp_eig = raw_eig[raw_eig>=0]
# Moments of population spectral distribution
colMeans(outer(pop_eig, 1:4, "^"))
# Estimators
moments_PSD(emp_eig, n-1, 4)