Quasi-Systematic Sampling From a Continuous Population

TL;DR

This paper introduces quasi-systematic point processes for sampling from a continuous population, allowing control over sample spread and enabling unbiased variance estimation, with practical algorithms and simulation validation.

Contribution

It presents a new family of quasi-systematic sampling processes with a tunable parameter, providing a flexible trade-off between sample spread and variance estimation accuracy.

Findings

Samples are well spread for large r

Unbiased variance estimators are available for all r > 0

Simulations demonstrate the method's effectiveness

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.