Determinantal Sampling Designs

Résumé

Determinantal point processes were introduced by physicists and probabilists in the 70's. They reappeared in the mathematical landscape at the beginnig of this century in the context of random matrices theory. Recently, they also attracted the attention of the statistical community, notably because of their repulsiveness. In a joint work with V. Loonis (Insee), we use them for survey sampling. In this talk, we will study more precisely this class of sampling designs, and the statistical properties of the associated estimator of a total. We will also construct determinantal sampling designs with specific properties (fixed size, optimality). Our results appeal to many mathematical theories: probability and statistics of course, but also linear algebra, frame theory and semi-definite optimization.