Wilhelm, Matthieu

2018-1-10, Tillé, Yves, Qualité, Lionel, Wilhelm, Matthieu

We present a new family of sampling designs in finite population based on the use of chain processes and of multivariate discrete distributions. In Bernoulli sampling, the number of non-selected units between two selected units has a geometric distribution, while, in simple random sampling, it has a negative hypergeometric distribution. We propose to replace these distributions by more general ones, which enables us to include a tuning parameter for the joint inclusion probabilities that have a relatively simple form. An effect of repulsion or attraction can then be added in the selection of the units in such a way that a large set of new designs are defined that include Bernoulli sampling, simple random sampling and systematic sampling. A set of simulations show the interest of the method.

2015-6-25, Wilhelm, Matthieu, Tillé, Yves

We present a family of sampling designs depending on a integer parameter r. Then, simple random sampling is a particular case of this sampling design, namely when r = 1 and the systematic sampling design is the limiting case when r tends to the infinity. For every r > 0, this sampling design has the important property to have first and second order densities which are tractable and positive. Thus, the Horvitz-Thompson estimator is unbiased and the estimator of the variance of the Horvitz-Thompson estimator is also unbiased. This family of sampling design can be used in finite population or on any finite interval of R.

2017-12-20, Tillé, Yves, Wilhelm, Matthieu

In this paper, we first aim to formalize the choice of the sampling design for a particular estimation problem. Next several principles are proposed: randomization, over-representation and restriction. These principles are fundamental to assist in the determination of the most appropriate design. A priori knowledge of the population can be also formalized by modelling the population, which can be helpful when choosing the sampling design. We present a list of sampling designs by specifying their corresponding models and the principles used to derive them. Emphasis is placed on new spatial sampling methods and their related models. A simulation shows the advantages of the different methods.

2017, Wilhelm, Matthieu, Qualité, Lionel, Tillé, Yves

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.