EstNull.func<-function (x,gamma=0.1)
{
 # x is a vector of z-values
 # gamma is a parameter, default is 0.1
 # output the estimated mean and standard deviation

 n = length(x)
 t = c(1:1000)/200
 
 gan    = n^(-gamma)
 that   = 0 
 shat   = 0
 uhat   = 0
 epshat = 0

 phiplus   = rep(1,1000)
 phiminus  = rep(1,1000)
 dphiplus  = rep(1,1000)
 dphiminus = rep(1,1000)
 phi       = rep(1,1000)
 dphi      = rep(1,1000)

 for (i in 1:1000) {
    s = t[i]
    phiplus[i]   = mean(cos(s*x))
    phiminus[i]  = mean(sin(s*x))
    dphiplus[i]  = -mean(x*sin(s*x))
    dphiminus[i] = mean(x*cos(s*x))
    phi[i]       = sqrt(phiplus[i]^2 + phiminus[i]^2)
 }

 ind = min(c(1:1000)[(phi - gan) <= 0])
 tt = t[ind]
 a  = phiplus[ind]
 b  = phiminus[ind]
 da = dphiplus[ind]
 db = dphiminus[ind]
 c  = phi[ind]

 that   = tt
 shat   = -(a*da + b*db)/(tt*c*c)
 shat   = sqrt(shat) 
 uhat   = -(da*b - db*a)/(c*c)
 epshat = 1 - c*exp((tt*shat)^2/2)

 return(musigma=list(mu=uhat,s=shat))
}