Quasi-Systematic Sampling From a Continuous Population
Abstract A specific family of point processes are introduced that allow to select samples for the purpose of estimating the mean or the integral of a function of a real variable. These processes, called quasi-systematic processes, depend on a tuning parameter $r>0$ that permits to control the likeliness of jointly selecting neighbor units in a same sample. When $r$ is large, units that are close tend to not be selected together and samples are well spread. When $r$ tends to infinity, the sampling design is close to systematic sampling. For all $r > 0$, the first and second-order unit inclusion densities are positive, allowing for unbiased estimators of variance.

Algorithms to generate these sampling processes for any positive real value of $r$ are presented. When $r$ is large, the estimator of variance is unstable. It follows that $r$ must be chosen by the practitioner as a trade-off between an accurate estimation of the target parameter and an accurate estimation of the variance of the parameter estimator. The method's advantages are illustrated with a set of simulations.
Keywords binomial process, point process, Poisson process, renewal process, systematic sampling.
Citation Wilhelm, M., Qualité, L., & Tillé, Y. (2017). Quasi-Systematic Sampling From a Continuous Population. Computational Statistics and Data Analysis, 105, 11-23.
Type Journal article (English)
Date of appearance 2017
Journal Computational Statistics and Data Analysis
Volume 105
Pages 11-23
URL https://arxiv.org/abs/1607.04993