varest {sampling}

Variance estimation using the Deville's method

Description

Computes the variance estimation of an estimator of the population total using the Deville's method.

Usage

varest(Ys,Xs=NULL,pik,w=NULL)

Arguments

Ys

vector of the variable of interest; its length is equal to n, the sample size.

Xs

matrix of the auxiliary variables; for the calibration estimator, this is the matrix of the sample calibration variables.

pik

vector of the first-order inclusion probabilities; its length is equal to n, the sample size.

w

vector of the calibrated weights (for the calibration estimator); its length is equal to n, the sample size.

Details

The function implements the following estimator:

\widehat{Var}(\widehat{Ys})=\frac{1}{1-\sum_{k\in s} a_k^2}\sum_{k\in s}(1-\pi_k)\left(\frac{y_k}{\pi_k}-\frac{\sum_{l\in s} (1-\pi_{l})y_l/\pi_l}{\sum_{l\in s} (1-\pi_l)}\right)

where a_k=(1-\pi_k)/\sum_{l\in s} (1-\pi_l).

References

Deville, J.-C. (1993). Estimation de la variance pour les enquêtes en deux phases. Manuscript, INSEE, Paris.

See Also

calibev

Examples

# Belgian municipalities data base
data(belgianmunicipalities)
attach(belgianmunicipalities)
# Computes the inclusion probabilities
pik=inclusionprobabilities(Tot04,200)
N=length(pik)
n=sum(pik)
# Defines the variable of interest
y=TaxableIncome
# Draws a Tille sample of size 200
s=UPtille(pik)
# Computes the Horvitz-Thompson estimator
HTestimator(y[s==1],pik[s==1])
# Computes the variance estimation of the Horvitz-Thompson estimator
varest(Ys=y[s==1],pik=pik[s==1])
# for an example using calibration estimator, see the 'calibration' vignette 
# vignette("calibration", package="sampling")