Simulation for Regression and Rao (1991) Estimator With Missing Data

 A Hint for Beginners 

It easy to evaluate performance any estimation procedure in simple random sampling by using a bootstrapping approaching, these codes are might be helpful for researchers (Errors or Omissions are expected).  

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library(sampling)

library(MASS)

##########################

sigma=matrix(c(6,3,3,8),2,2)

mu=c(0,1)

data=mvrnorm(10,mu,sigma);

x=data[,2];y=data[,1]

DF=data.frame(y,x)

N=nrow(DF);mx=mean(x);my=mean(y);sy=var(y);

sx=var(x);cxy=cov(x,y)/(mx*my);rhoxy=cor(y,x)

cx=sd(x)/mx;cy=sd(y)/my;

attach(DF)

####################################

n=50; r=30; N=1000; H=5000

##########################

thetarN=(1/r-1/N);thetarn=(1/r-1/n); 

#####################################

beta=cov(y,x)/sx

v1=(1)/(1+cy^2*(thetarN-thetarn*rhoxy^2))

v2=(my*cy*rhoxy)/(mx*cx*(1+cy^2*(thetarN-thetarn*rhoxy^2)))

###############################################

mxn=NULL;mxr=NULL;myn=NULL;myr=NULL;

################################

mxn=c();mxr=c();myn=c();myr=c();z1=c();z2=c();z3=c();

####################################

for(i in 1:H){

S1=DF[sample(1:N,   n,  replace=T),]

Sr=S1[sample(1:n, r, replace=T),]

mxn[i]=mean(S1$x);mxr[i]=mean(Sr$x);myr[i]=mean(Sr$y);

z1[i]=myr[i]

z2[i]=(myr[i]+beta*(mxn[i]-mxr[i]) )

z3[i]=(v1*myr[i]+v2*(mxn[i]-mxr[i]) )

}

mse1=(sum((z1-my)^(2)))/H

mse2=(sum((z2-my)^(2)))/H

mse3=(sum((z3-my)^(2)))/H

mse1/mse2*100;mse1/mse3*100;

   

For bootstrapping please visit

Simulations and Bootstrapping

 Thanks, Your suggestions will be appreciated