ddpca (version 1.1)

IHCDD: IHC-DD test

Description

Combining Innovated Higher Criticism with DDPCA for detecting sparse mean effect.

Usage

IHCDD(X, method = "nonconvex", K = 1, lambda = 3, max_iter_nonconvex = 15, 
SDD_approx = TRUE, max_iter_SDD = 20, eps = NA, rho = 20, max_iter_convex = 50, 
alpha = 0.5, pvalcut = NA)

Arguments

X

A \(n\times p\) data matrix, where each row is drawn i.i.d from \(\mathcal{N}(\mu,\Sigma)\)

method

Either "convex" or "noncovex", indicating which method to use for DDPCA.

K

Argument in function DDPCA_nonconvex. Need to be specified when method = "nonconvex"

lambda

Argument in function DDPCA_convex. Need to be specified when method = "convex"

max_iter_nonconvex

Argument in function DDPCA_nonconvex.

SDD_approx

Argument in function DDPCA_nonconvex.

max_iter_SDD

Argument in function DDPCA_nonconvex.

eps

Argument in function DDPCA_nonconvex.

rho

Argument in function DDPCA_convex.

max_iter_convex

Argument in function DDPCA_convex.

alpha

Argument in function HCdetection.

pvalcut

Argument in function HCdetection.

Value

Returns a list containing the following items

H

0 or 1 scalar indicating whether \(H_0\) the global null is rejected (1) or not rejected (0). Not recommended for use.

HCT

IHC-DD Test statistic

Details

See reference paper for more details.

References

Ke, Z., Xue, L. and Yang, F., 2019. Diagonally Dominant Principal Component Analysis. Journal of Computational and Graphic Statistics, under review.

See Also

DDHC, HCdetection, DDPCA_convex, DDPCA_nonconvex

Examples

# NOT RUN {
library(MASS)
n = 200
p = 200
k = 3
rho = 0.5
a = 0:(p-1)
Sigma_mu = rho^abs(outer(a,a,'-'))
Sigma_mu = (diag(p) + Sigma_mu)/2 # Now Sigma_mu is a symmetric diagonally dominant matrix
B = matrix(rnorm(p*k),nrow = p)
Sigma = Sigma_mu + B %*% t(B)
X = mvrnorm(n,rep(0,p),Sigma)
results = IHCDD(X,K = k)
print(results$H)
print(results$HCT)
# }