StratifiedSampling (version 0.4.1)

varEst: Estimator of the approximated variance for balanced sampling

Description

Estimator of the approximated variance for balanced sampling

Usage

varEst(X, strata, pik, s, y)

Value

a scalar, the value of the estimated variance.

Arguments

X

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

strata

A vector of integers that represents the categories.

pik

A vector of inclusion probabilities.

s

A sample (vector of 0 and 1, if rejected or selected).

y

A variable of interest.

Author

Raphaël Jauslin

Details

This function gives an estimator of the approximated variance of the Horvitz-Thompson total estimator presented by Hasler C. and Tillé Y. (2014).

References

Hasler, C. and Tillé, Y. (2014). Fast balanced sampling for highly stratified population. Computational Statistics and Data Analysis, 74:81-94.

See Also

varApp

Examples

N <- 1000
n <- 400
x1 <- rgamma(N,4,25)
x2 <- rgamma(N,4,25)

strata <- as.matrix(rep(1:40,each = 25)) # 25 strata
Xcat <- disjMatrix(strata)
pik <- rep(n/N,N)
X <- as.matrix(matrix(c(x1,x2),ncol = 2))
 
s <- stratifiedcube(X,strata,pik)
 
y <- 20*strata + rnorm(1000,120) # variable of interest
# y_ht <- sum(y[which(s==1)]/pik[which(s == 1)]) # Horvitz-Thompson estimator
# (sum(y_ht) - sum(y))^2 # true variance
varEst(X,strata,pik,s,y)
varApp(X,strata,pik,y)