# IHCDD: IHC-DD test In ddpca: Diagonally Dominant Principal Component Analysis

## Description

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

## Usage

 1 2 3 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}(μ,Σ) 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). Not recommended for use. HCT IHC-DD Test statistic

## Author(s)

Fan Yang <fyang1@uchicago.edu>

## References

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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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)