varHAJ | R Documentation |
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.
varHAJ(y, pik, s)
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. |
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.
A number, the variance
Tillé, Y. (2020). Sampling and estimation from finite populations. New York: Wiley
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