GGMridge (version 1.4)

getEfronp: Estimation of empirical null distribution.

Description

Estimation of empirical null distribution using Efron's central matching.

Usage

getEfronp(
  z,
  bins = 120L,
  maxQ = 9,
  pct = 0,
  pct0 = 0.25,
  cc = 1.2,
  plotIt = FALSE
)

Value

A list containing

correctz

The corrected z values to follow empirically standard normal distribution.

correctp

The corrected p values using the correct z values.

q

The chosen degree of polynomial for the estimated marginal density.

mu0hat

The location parameter for the normal null distribution.

sigma0hat

The scale parameter for the normal null distribution.

eta

The estimated null proportion.

Arguments

z

A numeric vector of z values following the theoretical normal null distribution.

bins

The number of intervals for density estimation of the marginal density of z.

maxQ

The maximum degree of the polynomial to be considered for density estimation of the marginal density of z.

pct

Low and top (pct*100) f(z).

pct0

Low and top (pct0*100) estimate f0(z).

cc

The central parts $$(\mu - \sigma cc, \mu + \sigma cc)$$ of the empirical distribution z are used for an estimate of the null proportion (eta).

plotIt

TRUE if density plot is to be produced.

Author

Min Jin Ha

References

Efron, B. (2004). Large-scale simultaneous hypothesis testing. Journal of the American Statistical Association, 99, 96--104.

Ha, M. J. and Sun, W. (2014). Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation. Biometrics, 70, 762--770.

Examples

 p <- 100 # number of variables
 n <- 50 # sample size

 ###############################
 # Simulate data
 ###############################
 simulation <- simulateData(G = p, etaA = 0.02, n = n, r = 1)
 data <- simulation$data[[1]]
 stddata <- scale(x = data, center = TRUE, scale = TRUE)
   
 ###############################
 # estimate ridge parameter
 ###############################
 lambda.array <- seq(from = 0.1, to = 20, by = 0.1) * (n - 1.0)
 fit <- lambda.cv(x = stddata, lambda = lambda.array, fold = 10L)
 lambda <- fit$lambda[which.min(fit$spe)] / (n - 1.0)
   
 ###############################
 # calculate partial correlation
 # using ridge inverse
 ###############################
 w.upper <- which(upper.tri(diag(p)))
 partial <- solve(lambda * diag(p) + cor(data))
 partial <- (-scaledMat(x = partial))[w.upper]
   
 ###############################
 # get p-values from empirical 
 # null distribution 
 ###############################
 efron.fit <- getEfronp(z = transFisher(x = partial))