epsest.func <- function(x,u,sigma)
{
  # x is a vector
  # u is the mean
  # sigma is the standard deviation

  z  = (x - u)/sigma
  xi = c(0:100)/100
  tmax=sqrt(log(length(x)))
  tt=seq(0,tmax,0.1)

  epsest=NULL

  for (j in 1:length(tt)) { 

    t=tt[j]
    f  = t*xi
    f  = exp(f^2/2)
    w  = (1 - abs(xi))
    co  = 0*xi

    for (i in 1:101) {
      co[i] = mean(cos(t*xi[i]*z));
    } 
    epshat = 1 - sum(w*f*co)/sum(w)
    epsest=c(epsest,epshat)
  }
  return(epsest=max(epsest))
}