StratifiedSampling (version 0.4.1)

varApp: Approximated variance for balanced sampling

Description

Approximated variance for balanced sampling

Usage

varApp(X, strata, pik, y)

Value

a scalar, the value of the approximated 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.

y

A variable of interest.

Author

Raphaël Jauslin

Details

This function gives an approximation of the variance of the Horvitz-Thompson total estimator presented by Hasler and Tillé (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

varEst

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)