@article {Schreuder:1990::1146,
title = "Notes: The Gain in Efficiency in ps Sampling over Poisson Sampling",
journal = "",
parent_itemid = "",
publishercode ="",
year = "1990",
volume = "36",
number = "4",
publication date ="1990-12-01T00:00:00",
pages = "1146-1152",
itemtype = "ARTICLE",
url = "https://www.ingentaconnect.com/content/saf/fs/1990/00000036/00000004/art00023",
keyword = "optimum linear model, Fixed sample, Hotvitz-Thompson",
author = "Schreuder, H. T.",
abstract = "A ratio is derived for the relative efficiency of mean-of-ratio estimation for ps sampling without replacement relative to Poisson sampling, assuming the model for which ps sampling with this estimator is optimum. This efficiency ratio is R = 1 + 1/ne where ne = the expected sample size in Poisson sampling and the sample size used in pps sampling. ps sampling from the cumulated x-values, a replacement sampling scheme, is compared to Poisson sampling in a simulation study using four sets of three populations, where two populations in each set are realizations of the optimal linear model for ps sampling with the Horvitz-Thompson estimator, and the third is an actual data set. The derived ratio is a good indicator of the gain in efficiency of ps sampling relative to Poission sampling. This is confirmed by simulation results from some populations. For. Sci. 36(4):1146-1152.",
}