StratifiedSampling (version 0.4.1)

vEst: Variance Estimation for balanced sample

Description

Estimated variance approximation calculated as the conditional variance with respect to the balancing equations of a particular Poisson design. See Tillé (2020)

Usage

vEst(Xauxs, piks, ys)

Value

Estimated variance of the horvitz-thompson estimator.

Arguments

Xauxs

A matrix of size (\(n\) x \(p\)) of auxiliary variables on which the sample must be balanced.

piks

A vector of inclusion probabilities. The vector has the size of the sample \(s\).

ys

A variable of interest.The vector has the size \(n\) of the sample \(s\).

Author

Raphaël Jauslin

References

Tillé, Y. (2020), Sampling and Estimation from finite populations, Wiley,

See Also

vDBS vApp

Examples

N <- 100 
n <- 40
x1 <- rgamma(N,4,25)
x2 <- rgamma(N,4,25)

pik <- rep(n/N,N)
Xaux <- cbind(pik,as.matrix(matrix(c(x1,x2),ncol = 2)))
Xspread <- cbind(runif(N),runif(N))
  

s <- balseq(pik,Xaux,Xspread)
  
y <- Xaux%*%c(1,1,3) + rnorm(N,120) # variable of interest
  
vEst(Xaux[s,],pik[s],y[s])
vDBS(Xaux[s,],Xspread[s,],pik[s],y[s])
vApp(Xaux,pik,y)