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Exponential inequalities for sampling designs

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02884292
Contributor : Guillaume Chauvet <>
Submitted on : Tuesday, October 20, 2020 - 11:25:08 AM
Last modification on : Sunday, October 25, 2020 - 3:09:44 AM

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  • HAL Id : hal-02884292, version 2
  • ARXIV : 2006.16600

Citation

Guillaume Chauvet, Mathieu Gerber. Exponential inequalities for sampling designs. 2020. ⟨hal-02884292v2⟩

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