Quasi-systematic sampling from a continuous population

A specific family of point processes is 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>0r>0 that permits to control the likeliness of jointly selecting neighbor units in a same sample. When rr is large, units that are close tend to not be selected together and samples are well spread. When rr tends to infinity, the sampling design is close to systematic sampling. For all r>0r>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 rr are presented. When rr is large, the estimator of variance is unstable. It follows that rr 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.