2016/07/18 by Matthieu Wilhelm, Wilhelm, Matthieu, Yves Tillé +3
Mathematics · Computer Science · #Point processes and geometric inequalities #Bayesian Methods and Mixture Models #Advanced Statistical Methods and Models
paper · pdf · doi:10.48550/arxiv.1607.04993
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.