varHAJ: Hajek-Rosen variance estimator

In WaveSampling: Weakly Associated Vectors (WAVE) Sampling

Hajek-Rosen variance estimator

Description

Estimator of the variance of the Horvitz-Thompson estimator. It is based on the variance estimator of the conditional Poisson sampling design. See Tillé (2020, Chapter 5) for more informations.

Usage

varHAJ(y, pik, s)

Arguments

y	vector of size n that represent the variable of interest.
pik	vector of the inclusion probabilities. The length should be equal to n.
s	index vector of size n with elements equal to the selected units.

Details

The function computes the following quantity :

v_{HAJ}(\widehat{Y}_{HT}) = \frac{n}{n-1} ∑_{k\in S} (1-π_k)≤ft( \frac{y_k}{π_k}-\frac{ ∑_{l\in S} (1-π_k)/π_k }{∑_{l\in S} (1-π_k) } \right)^2 .

This estimator is well-defined for maximum entropy sampling design and use only inclusion probabilities of order one.

Value

A number, the variance

References

Tillé, Y. (2020). Sampling and estimation from finite populations. New York: Wiley

WaveSampling documentation built on May 3, 2022, 1:07 a.m.