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 |