2020/06/30 by Guillaume Chauvet, Chauvet, Guillaume, Mathieu Gerber +1
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2006.16600
openalex publication_date 2020/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this work we introduce a general approach, based on the mar-tingale representation of a sampling design and Azuma-Hoeffding's inequality , to derive exponential inequalities for the difference between a Horvitz-Thompson estimator and its expectation. Applying this idea, we establish such inequalities for Chao's procedure, Tillé's elimination procedure, the generalized Midzuno method as well as for Brewer's method. As a by-product, we prove that the first three sampling designs are (conditionally) negatively associated. For such sampling designs, we show that that the inequality we obtain is usually sharper than the one obtained by applying known results for negatively associated random variables.