This paper provides refined versions of some known functional central limit theorems for conditional Poisson sampling which are more suitable for applications. The theorems presented in this paper are generalizations of some results that have been recently published by Bertail, Chautru, and Clémençon [1]. The asymptotic equicontinuity part of the proofs presented in this paper is based on the same idea as in [1] but some of the missing details are provided. On the way to the functional central limit theorems, this paper provides a detailed discussion of what must be done in order to prove conditional and unconditional weak convergence in bounded function spaces in the context of survey sampling. The results from this discussion can be useful to prove further weak convergence results.

Pasquazzi, L. (2019). Functional Central Limit Theorems for Conditional Poisson sampling Designs [Working paper].

Functional Central Limit Theorems for Conditional Poisson sampling Designs

Pasquazzi, L
2019

Abstract

This paper provides refined versions of some known functional central limit theorems for conditional Poisson sampling which are more suitable for applications. The theorems presented in this paper are generalizations of some results that have been recently published by Bertail, Chautru, and Clémençon [1]. The asymptotic equicontinuity part of the proofs presented in this paper is based on the same idea as in [1] but some of the missing details are provided. On the way to the functional central limit theorems, this paper provides a detailed discussion of what must be done in order to prove conditional and unconditional weak convergence in bounded function spaces in the context of survey sampling. The results from this discussion can be useful to prove further weak convergence results.
Working paper
weak convergence, empirical process, conditional Poisson sampling, uniform entropy condition
English
2019
https://arxiv.org/abs/1905.01021
arXiv:1905.01021 [math.ST]
Pasquazzi, L. (2019). Functional Central Limit Theorems for Conditional Poisson sampling Designs [Working paper].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/233607
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