Est_Mean_Hajek: The Hajek estimator for a mean
In samplingVarEst: Sampling Variance Estimation

Est.Mean.Hajek

R Documentation

The Hajek estimator for a mean

Description

Computes the Hajek (1971) estimator for a population mean.

Usage

Est.Mean.Hajek(VecY.s, VecPk.s)

Arguments

`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`. There must not be missing values.
`VecPk.s`	vector of the first-order inclusion probabilities; its length is equal to n, the sample size. Values in `VecPk.s` must be greater than zero and less than or equal to one. There must not be missing values.

Details

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.

Value

The function returns a value for the mean 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.

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
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

samplingVarEst documentation built on Jan. 14, 2023, 5:08 p.m.