R/beta_AD.R

In COR: The COR for Optimal Subset Selection in Distributed Estimation

#' Caculate the estimators of beta on the A-opt and D-opt
#'
#' @param K is the number of subsets
#' @param nk is the length of subsets
#' @param alpha is the significance level
#' @param X is the observation matrix
#' @param y is the response vector
#' 
#' @return betaA, betaD
#' @export

#' @examples 
#'  p=6;n=1000;K=2;nk=200;alpha=0.05;sigma=1
#'  e=rnorm(n,0,sigma); beta=c(sort(c(runif(p,0,1)))); 
#'  data=c(rnorm(n*p,5,10));X=matrix(data, ncol=p);
#'  y=X%*%beta+e;
#'  beta_AD(K=K,nk=nk,alpha=alpha,X=X,y=y)

beta_AD=function(K=K,nk=nk,alpha=alpha,X=X,y=y){
  n=nrow(X);p=ncol(X)
  M=W=c(rep(1,K));
  mr=matrix(rep(0,K*nk),ncol=nk)
  R=matrix(rep(0,n*nk), ncol=n);Io=matrix(rep(0,nk*K), ncol=nk);
  for (i in 1:K){ 
    mr[i,]=sample(1:n,nk,replace=T);
    r=matrix(c(1:nk,mr[i,]),ncol=nk,byrow=T);
    R[t(r)]=1
    Io[i,]=r[2,]
    X1=R%*%X;y1=R%*%y;
    ux=solve(crossprod(X1)) 
    W[i]= sum(diag(t(ux)%*% ux))
    M[i]=  det(X1%*%t(X1))
  }
  XD= X[Io[which.max(M),],];yD= y[Io[which.max(M),]]
  betaD=solve(crossprod(XD))%*%t(XD)%*% yD
  XA= X[Io[which.min(W),],];yA= y[Io[which.min(W),]] 
  betaA=solve(crossprod(XA))%*%t(XA)%*% yA
  return(list(betaA=betaA,betaD=betaD))
}