##########################################################
#This function takes data set and marker positions(pos)
#Deltahat is obtained by sum(LI)/sum(I).
#After fixing delta = deltahat, lambdahat is set to be the value
#which maximizes log-likelihood. (nlminb is used for maximization)
#It returns deltahat, lambdahat,
#phat (proportion of informative markers) and log-likelihood evaluated at
#deltahat, and lambdahat

simple.est.null<-function(data,pos){
  LI<-apply(data,2,function(x){sum(x==1)})
  I<-apply(data,2,function(x){sum(x!=-1)})
  
  deltahat<- sum(LI)/sum(I)
  phat<-sum(I)/nrow(data)/length(pos) # proportion of informative markers
    
  profile<-nlminb(start=0,mloglik.null,delta=deltahat,data=data,pos=pos,
		   lower=-Inf,upper=Inf)
  
  message<-profile$message

  lambdahat<-1/exp(profile$parameters)
  loglik.null<-(-profile$objective)
  
  return(list(deltahat=deltahat,lambdahat=lambdahat,phat=phat,
	      loglik.null=loglik.null,message=message))
}


######## Example ######################################

pro<-dget("pro.data")
thy<-dget("thy.data")
fjp<-dget("fjp.data")

pro.simple.est.null<-simple.est.null(data=pro$data, pos=pro$pos)
thy.simple.est.null<-simple.est.null(data=thy$data, pos=thy$pos)
fjp.simple.est.null<-simple.est.null(data=fjp$data, pos=fjp$pos)


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