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Abstract
A balanced sampling design should always be the adopted strategy if auxiliary information is available. In addition, integrating a stratified structure of the population in the sampling process can considerably reduce the variance of the estimators. We propose here a new method to handle the selection of a balanced sample in a highly stratified population. The method improves substantially the commonly used sampling designs and reduces the time-consuming problem that could arise if inclusion probabilities within strata do not sum to an integer.
Highlights
In survey statistics, balanced sampling is a efficient method when values of auxiliary variables are available for all units in the population
The properties of the cube method imply that the inclusion probabilities are satisfied and that the sample is balanced on the auxiliary variables in these two methods
The stratified sampling procedure is a well-known and appropriate procedure to reduce the variance of the Horvitz–Thompson estimator
Summary
In survey statistics, balanced sampling is a efficient method when values of auxiliary variables are available for all units in the population. The balanced and stratified sampling method of Chauvet (2009) has been improved by Hasler and Tillé (2014) to partially resolve the disadvantage of the time required to process a highly stratified population. When the sum of the inclusion probabilities in the strata is not an integer, the computation time can become problematic This problem arises, for example, when the objective is to select less than one individual per household. We propose a new method to obtain a stratified balanced sample. This new method is interesting when the population is highly stratified and the inclusion probabilities do not sum to an integer within the strata.
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