Variance estimation using the Deville's method
Computes the variance estimation of an estimator of the population total using the Deville's method.
varest(Ys,Xs=NULL,pik,w=NULL)
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. |
The function implements the following estimator:
\widehat{Var}(\widehat{Ys})=\frac{1}{1-∑_{k\in s} a_k^2}∑_{k\in s}(1-π_k)≤ft(\frac{y_k}{π_k}-\frac{∑_{l\in s} (1-π_{l})y_l/π_l}{∑_{l\in s} (1-π_l)}\right)
where a_k=(1-π_k)/∑_{l\in s} (1-π_l).
Deville, J.-C. (1993). Estimation de la variance pour les enquêtes en deux phases. Manuscript, INSEE, Paris.
# 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")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.