Est.Total.Hajek | R Documentation |
Computes the Hajek (1971) estimator for a population total.
Est.Total.Hajek(VecY.s, VecPk.s, N)
VecY.s |
vector of the variable of interest; its length is equal to n, the sample size. Its length has to be the same as that of |
VecPk.s |
vector of the first-order inclusion probabilities; its length is equal to n, the sample size. Values in |
N |
the population size. It must be an integer or a double-precision scalar with zero-valued fractional part. |
For the population total of the variable y:
t = ∑_{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{∑_{k\in s} w_k y_k}{∑_{k\in s} w_k}
where w_k=1/π_k and π_k denotes the inclusion probability of the k-th element in the sample s.
The function returns a value for the total point estimator.
Emilio Lopez Escobar.
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.
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
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
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