#simulaiton using GLR to test sigma=0

  simulation1<-function(m,tt){
  set.seed(1234123)
  times<-0
    for(i in 1:tt){
    y<-rep(.5,5*m)
    
#generate epsilon from normal distribution

    epsilon<-rnorm(5*m,0,1)      
    y<-y+epsilon
    
    #print (y)
#estimators
    uhat<-mean(y)
    tauhat0<-sum((y-uhat)^2)/(m*5)
    #print (uhat)
   #    print (tauhat0)
   
 temp1<-NULL
 temp2<-0  
        for(j in 1:m){
       temp3<-y[((j-1)*5+1):((j-1)*5+5)]
       temp4<-mean(temp3)
       temp5<-sum((temp3-temp4)^2)
       temp2<-temp2+temp5
       temp1<-c(temp1,temp4)
    }
    tauhat<-temp2/(m*4)
    temp6<-sum((temp1-uhat)^2)
    sigmahat<-max(0,((5/m)*temp6-tauhat)/5)
    #print(uhat)
#    print(tauhat0)
#    print(tauhat)
#    print(sigmahat)
    n<-5*m
# teststatistics
    R<-n*log(tauhat0)+n-(n-m)*log(tauhat)-m*log(tauhat+5*sigmahat)-
    n*tauhat0/tauhat+(sigmahat/tauhat)*(25/(tauhat+5*sigmahat))*temp6
    #qchisq(.95,1)=3.841459
    if(R<3.841459){times<-times+1} 
    
  #print (R)
    }
    
   result<-times/tt
result
}