AEB: AEB

In OPTtesting: Optimal Testing

AEB

Description

Estimate the parameters in the three-part mixture

Usage

AEB(
  Z,
  Sigma,
  eig = eigs_sym(Sigma, min(400, length(Z)), which = "LM"),
  eig_tol = 1,
  set_nu = c(0),
  set1 = c(0:10) * 0.01 + 0.01,
  set2 = c(0:10) * 0.01 + 0.01,
  setp = c(1:7) * 0.1
)

Arguments

Z	a vector of test statistics
Sigma	covariance matrix
eig	eig value information
eig_tol	the smallest eigen value used in the calulation
set_nu	a search region for nu_0
set1	a search region for tau_sqr_1
set2	a search region for tau_sqr_2
setp	a search region for proportion

Details

Estimate the parameters in the three-part mixture Z|μ ~ N_p(μ,Σ ) where μ_i ~ π_0 δ_ {ν_0} + π_1 N(μ_1, τ_1^2) + π_2 N(μ_2, τ_2^2), i = 1, ..., p

Value

The return of the function is a list in the form of list(nu_0, tau_sqr_1, tau_sqr_2, pi_0, pi_1, pi_2, mu_1, mu_2, Z_hat).

nu_0, tau_sqr_1, tau_sqr_2: The best combination of (ν_0, τ_1^2, τ_2^2) that minimize the total variance from the regions (D_{ν_0}, D_{τ_1^2}, D_{τ_2^2}).

pi_0, pi_1, pi_2, mu_1, mu_2: The estimates of parameters π_0, π_1, π_2, μ_1, μ_2.

Z_hat: A vector of simulated data base on the parameter estimates.

Examples

p = 500
 n_col = 10
A = matrix(rnorm(p*n_col,0,1), nrow = p, ncol = n_col, byrow = TRUE)
Sigma = A %*% t(A) +diag(p)
Sigma = cov2cor(Sigma) #covariance matrix
Z = rnorm(p,0,1) #this is just an example for testing the algorithm.
#Not true test statistics with respect to Sigma
best_set =  AEB(Z,Sigma)
print(c(best_set$pi_0, best_set$pi_1, best_set$pi_2, best_set$mu_1, best_set$mu_2))

library(MASS)
######################################
#construct a test statistic vector Z
p = 1000
n_col = 4
pi_0 = 0.6
pi_1 = 0.2
pi_2 = 0.2
nu_0 = 0
mu_1 = -1.5
mu_2 = 1.5
tau_sqr_1 = 0.1
tau_sqr_2 = 0.1


A = matrix(rnorm(p*n_col,0,1), nrow = p, ncol = n_col, byrow = TRUE)
Sigma = A %*% t(A) +diag(p)
Sigma = cov2cor(Sigma) #covariance matrix




b = rmultinom(p, size = 1, prob = c(pi_0,pi_1,pi_2))
ui = b[1,]*nu_0 + b[2,]*rnorm(p, mean = mu_1,
     sd = sqrt(tau_sqr_1)) + b[3,]*rnorm(p, mean = mu_2,
      sd = sqrt(tau_sqr_2)) # actual situation
Z = mvrnorm(n = 1,ui, Sigma, tol = 1e-6, empirical = FALSE, EISPACK = FALSE)

best_set =AEB(Z,Sigma)
print(c(best_set$pi_0, best_set$pi_1, best_set$pi_2, best_set$mu_1, best_set$mu_2))

OPTtesting documentation built on May 26, 2022, 5:09 p.m.