Est.Mean.Hajek | R Documentation |
Computes the Hajek (1971) estimator for a population mean.
Est.Mean.Hajek(VecY.s, VecPk.s)
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 |
For the population mean of the variable y:
\bar{y} = \frac{1}{N} ∑_{k\in U} y_k
the approximately unbiased Hajek (1971) estimator of \bar{y} (implemented by the current function) is given by:
\hat{\bar{y}}_{Hajek} = \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 mean 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.Mean.NHT
VE.Jk.Tukey.Mean.Hajek
VE.Jk.CBS.HT.Mean.Hajek
VE.Jk.CBS.SYG.Mean.Hajek
VE.Jk.B.Mean.Hajek
VE.Jk.EB.SW2.Mean.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 y1 <- oaxaca$POP10 #Defines the variable of interest y1 y2 <- oaxaca$HOMES10 #Defines the variable of interest y2 Est.Mean.Hajek(y1[s==1], pik.U[s==1]) #Computes the Hajek est. for y1 Est.Mean.Hajek(y2[s==1], pik.U[s==1]) #Computes the Hajek est. for y2
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.