DDHC {ddpca}

DD-HC test

Description

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

Usage

DDHC(X, known_Sigma = NA, 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)

known_Sigma

The true covariance matrix of data. Default NA. If NA, then \Sigma will be estimated from data matrix X.

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.

Details

See reference paper for more details.

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). The use of H is not recommended as it's approximately valid only when p is sufficiently large and mean effect in alternative is really sparse.

HCT

DD-HC Test statistic

Author(s)

Fan Yang <[e-mail]>

References

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

See Also

IHCDD, HCdetection, DDPCA_convex, DDPCA_nonconvex

Examples

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 = DDHC(X,K = k)
print(results$H)
print(results$HCT)