Читать книгу Sampling and Estimation from Finite Populations - Yves Tille - Страница 47
Proof:
ОглавлениеIt is also possible to write the expansion estimator with a vector notation. Let be the vector of dilated values:
This vector only exists if all the inclusion probabilities are nonzero. We can then write
The calculation of the variance is then immediate:
If the sample is of fixed sample size, Sen (1953) and Yates & Grundy (1953) have shown the following result:
