Empirical Processes in Survey Sampling with (Conditional) Poisson Designs

It is the main purpose of this paper to study the asymptotics of certain variants of the empirical process in the context of survey data. Specifically, Functional Central Limit Theorems are established under usual conditions when the sample is drawn from a Poisson or a rejective sampling design. The...

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Bibliographic Details
Published inScandinavian journal of statistics Vol. 44; no. 1; pp. 97 - 111
Main Authors BERTAIL, PATRICE, CHAUTRU, EMILIE, CLÉMENÇON, STEPHAN
Format Journal Article
LanguageEnglish
Published Oxford Wiley Publishing 01.03.2017
Blackwell Publishing Ltd
Wiley
Subjects
Analysis
Asymptotic methods
Asymptotic properties
Design optimization
empirical processes
functional central limit theorem
Functionals
Inclusions
Machine Learning
Mathematics
Poisson design
Poisson distribution
Probability
rejective design
Samples
Sampling
Statistical analysis
Statistics
Studies
survey sampling
Poisson design
survey sampling
rejective design
functional central limit theorem
empirical processes
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Summary:It is the main purpose of this paper to study the asymptotics of certain variants of the empirical process in the context of survey data. Specifically, Functional Central Limit Theorems are established under usual conditions when the sample is drawn from a Poisson or a rejective sampling design. The framework we develop encompasses sampling designs with non-uniform first order inclusion probabilities, which can be chosen so as to optimize estimation accuracy. Applications to Hadamard differentiable functionals are considered.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12243