calibev: Calibration estimator and its variance estimation

Description

Computes the calibration estimator and its variance estimation using the residuals' technique. The function returns two values: cest (the calibration estimator) and evar (its estimated variance).

Usage

calibev(Ys,Xs,total,pikl,d,g,q=rep(1,length(d)), with=FALSE,EPS=1e-6)

Arguments

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

matrix of sample calibration variables.

total

vector of population totals for calibration.

pikl

matrix of joint inclusion probabilities of the sample units.

vector of initial weights of the sample units.

vector of g-weights; its size is n, the sample size.

vector of positive values accounting for heteroscedasticity; its size is n, the sample size.

with

if TRUE, the variance estimation takes into account the initial weights d; otherwise, the final weights w=g*d are taken into account; by default, its value is FALSE. If TRUE, the following formula is used $$Var(Ys)= \sum_{k\ins}\s

EPS

the tolerance in checking the calibration; by default, its value is 1e-6.

encoding

latin1

References

Deville, J.-C. and S�arndal, C.-E. (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association, 87:376--382. Deville, J.-C., S�rndal, C.-E., and Sautory, O. (1993). Generalized raking procedure in survey sampling. Journal of the American Statistical Association, 88:1013--1020.

Examples

Run this code

############
## Example
############
# Example of g-weights (linear, raking, truncated, logit),
# with the data of Belgian municipalities as population.
# Firstly, a sample is selected by means of Poisson sampling.
# Secondly, the g-weights are calculated.
data(belgianmunicipalities)
attach(belgianmunicipalities)
# matrix of calibration variables for the population
X=cbind(
Men03/mean(Men03),
Women03/mean(Women03),
Diffmen,
Diffwom,
TaxableIncome/mean(TaxableIncome),
Totaltaxation/mean(Totaltaxation),
averageincome/mean(averageincome),
medianincome/mean(medianincome))
# selection of a sample with expectation size equal to 200
# by means of Poisson sampling
# the inclusion probabilities are proportional to the average income 
pik=inclusionprobabilities(averageincome,200)
N=length(pik)               # population size
s=UPsystematic(pik)  	    # draws a sample s using systematic sampling	
Xs=X[s==1,]                 # matrix of sample calibration variables
piks=pik[s==1]              # sample inclusion probabilities
n=length(piks)              # sample size
# vector of population totals of the calibration variables
total=c(t(rep(1,times=N))%*%X)  
g1=calib(Xs,d=1/piks,total,method="linear") # computes the g-weights
pikl=UPsystematicpi2(pik)   # computes the matrix of the joint inclusion probabilities 
pikls=pikl[s==1,s==1]       # the same matrix for the units in s
Ys=Tot04[s==1]		    # the variable of interest is Tot04	(for the units in s)
calibev(Ys,Xs,total,pikls,d=1/piks,g1,with=FALSE,EPS=1e-6)