R/package-jipApprox.R

#' jipApprox: Approximate inclusion probabilities for survey sampling
#'
#' @description
#' Approximate joint-inclusion probabilities in Unequal Probability Sampling,
#' or compute Monte Carlo approximations of the first and second-order inclusion
#' probabilities of a general sampling design as in Fattorini (2006)
#' <doi:10.1093/biomet/93.2.269>.
#'
#' @section Approximation of Joint-inclusion probabilities:
#' Function \code{\link{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
#' function \code{\link{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 \code{\link{HTvar}}.
#'
#'
#'
#'
#' @references
#'
#' 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
#'
#'
#' @importFrom stats rmultinom runif
#' @importFrom utils combn setTxtProgressBar txtProgressBar write.table
"_PACKAGE"

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jipApprox documentation built on Aug. 26, 2023, 9:06 a.m.