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Exponential inequalities for sampling designs

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  • Chauvet, Guillaume
  • Gerber, Mathieu

Abstract

In this work, we introduce an approach based on the martingale 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. We derive a new exponential inequality for conditionally negatively associated (CNA) sampling designs, which is shown to improve over two existing inequalities that can be used in this context. We establish that Chao’s procedure, Tillé’s elimination procedure and the generalized Midzuno method are CNA sampling designs, and thus obtain an exponential inequality for these three sampling procedures. We show that our approach is useful beyond CNA sampling designs by deriving an exponential inequality for Brewer’s method.

Suggested Citation

  • Chauvet, Guillaume & Gerber, Mathieu, 2026. "Exponential inequalities for sampling designs," Statistics & Probability Letters, Elsevier, vol. 232(C).
    • Handle: RePEc:eee:stapro:v:232:y:2026:i:c:s0167715226000180
    DOI: 10.1016/j.spl.2026.110654
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    References listed on IDEAS

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    1. Qi-Man Shao, 2000. "A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 13(2), pages 343-356, April.
    2. Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
    3. Petter Brändén & Johan Jonasson, 2012. "Negative Dependence in Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 830-838, December.
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