#ARM-Tweedie

#################input################
#######parameters
#K: number of candidate models
#rept: number of data splittings
####### data for training the model averaging weights
#Pred_Candidate: n by K matrix of predictions, each row representing a candidate prediction
#y: n by 1 vector, the true value of the repsonse 





library(Tweedie)
ARMT=function(K, rept, Pred_Candidate,y){
w=matrix(NA,rept,K)
n=nrow(X)
n0=floor(n/2)
for (j in 1:rept){
  index_trainn=sample(n,n0)
  for(i in 1:K){
    tt=(y[index_trainn]-Pred_Candidate[index_trainn,i])
    tt1=(y[-index_trainn]-Pred_Candidate[-index_trainn,i])
    CC <- sum(tt1^2)/2
    CC1<- sum(abs(tt1))
    sigmahat=sqrt(sum(tt^2)/n0)
    sigmahat1=sum(abs(tt))/n0
    w[j,i]=sum(log(dtweedie(y[-index_trainn],mu=(abs(Pred_Candidate[-index_trainn,i])+1)^(0.5),phi=var(y[index_trainn])/mean(y[index_trainn])^1.5,power=1.5)))
    

  }
  w[j,]=exp(w[j,]-max(w[j,]))
  w[j,]=w[j,]/sum(w[j,])
  w1=colMeans(w)
  
}
#returning the ARM-Tweedie weights
return(w1)
}

#all_predictions_candidate: N by K matrix that contains all the candidate predictions of your data
#The ARM-tweedie estimator is as follows.
pred_ARM_tweedie=as.matrix(all_predictions_candidate)%*%w1