Sharp exponential inequalities in survey sampling: conditional Poisson sampling schemes - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

Sharp exponential inequalities in survey sampling: conditional Poisson sampling schemes

Résumé

This paper is devoted to establishing exponential bounds for the probabilities of deviation of a sample sum from its expectation, when the variables involved in the summation are obtained by sampling in a finite population according to a rejective scheme, generalizing sampling without replacement, and by using an appropriate normalization. In contrast to Poisson sampling, classical deviation inequalities in the i.i.d. setting do not straightforwardly apply to sample sums related to rejective schemes, due to the inherent dependence structure of the sampled points. We show here how to overcome this difficulty, by combining the formulation of rejective sampling as Poisson sampling conditioned upon the sample size with the Escher transformation. In particular, the Bennett/Bernstein type bounds established highlight the effect of the asymptotic variance σ 2 N of the (properly standardized) sample weighted sum and are shown to be much more accurate than those based on the negative association property shared by the terms involved in the summation. Beyond its interest in itself, such a result for rejective sampling is crucial, insofar as it can be extended to many other sampling schemes, namely those that can be accurately approximated by rejective plans in the sense of the total variation distance .
Fichier principal
Vignette du fichier
1610.03776 (1).pdf (250.35 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01707442 , version 1 (12-02-2018)

Identifiants

  • HAL Id : hal-01707442 , version 1

Citer

Patrice Bertail, Stéphan Clémençon. Sharp exponential inequalities in survey sampling: conditional Poisson sampling schemes. 2018. ⟨hal-01707442⟩
71 Consultations
387 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More