R/quantil_ord.R

In mht: Multiple Hypothesis Testing for Variable Selection in High-Dimensional Linear Models

# Author : F.Rohart,  Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, Brisbane, QLD
# created: pre 01-01-2013
# last modification: 10-10-2014
# Copyright (C) 2014
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 2
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

quantil_ord=function(n,p,k,alpha,IT,sigma)
{
	if(missing(alpha)){alpha=c(0.1,0.05)}
	if(missing(IT)){IT=20000}
	if(missing(sigma)){sigma=0}
	if(sigma<0){stop("sigma<0? Really?")}
	if(missing(n)||(missing(p))||(missing(k))){stop("something is missing, either n or p or k")}

    #simulation pour trouver \alpham
    FF=numeric(0)


    if(sigma==0)
    {
        for(i in 1:IT)
        {
            eps=as.matrix(rnorm(n))
            F=numeric(0)
            for(m in 0:(log(min(n,p)-k-1,2)-1))
            {
                A=(n-k-2^m)*sum(eps[(k+1):(k+2^m)]^2)/(2^m*sum((eps[(k+2^m+1):n])^2))
                F[m+1]=1-pf(A,2^m,n-k-2^m)
            }
            FF[i]=min(F)
        }
    }else{
        for(i in 1:IT)
        {
            eps=as.matrix(rnorm(n,sd=sqrt(sigma)))
            F=numeric(0)
            for(m in 0:(log(min(n,p)-k-1,2)-1))
            {
                A=sum(eps[(k+1):(k+2^m)]^2)/sigma
                F[m+1]=1-pchisq(A,2^m)
            }
            FF[i]=min(F)
        }
    }

    alph=numeric(0)
    for(i in 1:length(alpha))
    {
        alph=c(alph,quantile(FF,alpha[i]))
    }
        

    return(list(quantile=alph))
}