jipApprox: Approximate inclusion probabilities for survey sampling
jip_approx provides a number of approximations of the
second-order inclusion probabilities that require only the first-order inclusion
probabilities. These approximations may be employed in unequal probability sampling
design with high entropy. A more flexible approximation may be obtained by using
jip_MonteCarlo, which estimates inclusion probabilities
through a Monte Carlo simulation.
The variance of the Horvitz-Thompson total estimator may be then estimated by
plugging the approximated joint probabilities into the Horvitz-Thompson or
Sen-Yates-Grundy variance estimator using function
Matei, A.; Tillé, Y., 2005. Evaluation of variance approximations and estimators in maximum entropy sampling with unequal probability and fixed sample size. Journal of Official Statistics 21 (4), 543-570.
Haziza, D.; Mecatti, F.; Rao, J.N.K. 2008. Evaluation of some approximate variance estimators under the Rao-Sampford unequal probability sampling design. Metron LXVI (1), 91-108.
Fattorini, L. 2006. Applying the Horvitz-Thompson criterion in complex designs: A computer-intensive perspective for estimating inclusion probabilities. Biometrika 93 (2), 269–278
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