Est.Total.Hajek {samplingVarEst} | R Documentation |
The Hajek estimator for a total
Description
Computes the Hajek (1971) estimator for a population total.
Usage
Est.Total.Hajek(VecY.s, VecPk.s, N)
Arguments
VecY.s |
vector of the variable of interest; its length is equal to |
VecPk.s |
vector of the first-order inclusion probabilities; its length is equal to |
N |
the population size. It must be an integer or a double-precision scalar with zero-valued fractional part. |
Details
For the population total of the variable y
:
t = \sum_{k\in U} y_k
the approximately unbiased Hajek (1971) estimator of t
(implemented by the current function) is given by:
\hat{t}_{Hajek} = N \frac{\sum_{k\in s} w_k y_k}{\sum_{k\in s} w_k}
where w_k=1/\pi_k
and \pi_k
denotes the inclusion probability of the k
-th element in the sample s
.
Value
The function returns a value for the total point estimator.
Author(s)
Emilio Lopez Escobar.
References
Hajek, J. (1971) Comment on An essay on the logical foundations of survey sampling by Basu, D. in Foundations of Statistical Inference (Godambe, V.P. and Sprott, D.A. eds.), p. 236. Holt, Rinehart and Winston.
See Also
Est.Total.NHT
VE.Jk.Tukey.Total.Hajek
VE.Jk.CBS.HT.Total.Hajek
VE.Jk.CBS.SYG.Total.Hajek
VE.Jk.B.Total.Hajek
VE.Jk.EB.SW2.Total.Hajek
Examples
data(oaxaca) #Loads the Oaxaca municipalities dataset
pik.U <- Pk.PropNorm.U(373, oaxaca$HOMES00) #Reconstructs the 1st order incl. probs.
s <- oaxaca$sHOMES00 #Defines the sample to be used
N <- dim(oaxaca)[1] #Defines the population size
y1 <- oaxaca$POP10 #Defines the variable y1
y2 <- oaxaca$HOMES10 #Defines the variable y2
Est.Total.Hajek(y1[s==1], pik.U[s==1], N) #The Hajek estimator for y1
Est.Total.Hajek(y2[s==1], pik.U[s==1], N) #The Hajek estimator for y2