Determinantal Sampling Designs

TL;DR

This paper introduces determinantal sampling designs, a new class of sampling methods based on point processes, providing exact variance formulas, construction algorithms, and optimal design search strategies.

Contribution

It defines and analyzes determinantal sampling designs, offering explicit construction methods and variance computations, advancing sampling theory with novel mathematical tools.

Findings

Exact variance formulas for linear estimators

Explicit algorithms for fixed size designs

Asymptotic and finite sample theorems

Abstract

In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple selection algorithm. We compute exactly the variance of linear estimators constructed upon these designs by using the first and second order inclusion probabilities. Moreover, we obtain asymptotic and finite sample theorems. We construct explicitly fixed size determinantal sampling designs with given first order inclusion probabilities. We also address the search of optimal determinantal sampling designs.