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#' Caculate the estimator on the Mean method
#'
#' @param data is the orignal data set
#' @param data0 is the missing data set
#' @param real is to judge whether the data set is a real missing data set
#' @param example is to judge whether the data set is a simulation example.
#'
#' @return XMean, MSEMean, MAEMean, REMean, GCVMean
#' @export
#'
#' @examples
#' library(MASS)
#' n=100;p=10;per=0.1
#' X0=data=matrix(mvrnorm(n*p,0,1),n,p)
#' m=round(per*n*p,digits=0)
#' mr=sample(1:(n*p),m,replace=FALSE)
#' X0[mr]=NA;data0=X0
#' Mean(data=data,data0=data0,real=FALSE,example=FALSE)
#the Mean method
Mean=function(data=0,data0,real=TRUE,example=FALSE)
#It defaults that the data set is a real data set
{#1
if (real||example){#2
etatol=0.7
}else{#2
etatol=0.9
}#2
X0=data0
n=nrow(X0);p=ncol(X0)
mr=which(is.na(X0)==TRUE)
m=nrow(as.matrix(mr))
cm0=colMeans(X0,na.rm=T)
ina=as.matrix(mr%%n)
jna=as.matrix(floor((mr+n-1)/n))
data0[is.na(data0)]=cm0[ceiling(which(is.na(X0))/n)]
XMean=Xnew=as.matrix(data0)
for (j in 1:p){#2
Mj=is.na(X0[,j])
iob=which(Mj==FALSE)
chj=sum(abs(round(X0[iob,j])-X0[iob,j]))
if (chj==0){#3
XMean[,j]=round(XMean[,j])
}else{#3
XMean[,j]= XMean[,j]
}#3
}#2
if(real){#2
MSEMean= MAEMean= REMean='NULL'
}else{#2
MSEMean=(1/m)*t(Xnew[mr]-data[mr])%*%(Xnew[mr]-data[mr])
MAEMean=(1/m)*sum(abs(Xnew[mr]-data[mr]))
REMean=(sum(abs(data[mr]-Xnew[mr])))/(sum(data[mr]))
}#2
lambdaMean=svd(cor(XMean))$d
lMean=lambdaMean/sum(lambdaMean);J=rep(lMean,times=p);dim(J)=c(p,p)
upper.tri(J,diag=T);J[lower.tri(J)]=0;J;dim(J)=c(p,p)
etaMean=matrix(colSums(J),nrow = 1,ncol = p,byrow = FALSE)
wwMean=which(etaMean>=etatol);kMean=wwMean[1]
lambdaMeanpk=lambdaMean[(kMean+1):p]
GCVMean=sum(lambdaMeanpk)*p/(p-kMean)^2
return(list(XMean=XMean,MSEMean=MSEMean,MAEMean=MAEMean,REMean=REMean,GCVMean=GCVMean))
}#1
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