Variance Estimation Using Linearization for Poverty and Social Exclusion Indicators

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Eric Graf and Yves Tillé^{Note 1}

Abstract

We have used the generalized linearization technique based on the concept of influence function, as Osier has done (Osier 2009), to estimate the variance of complex statistics such as Laeken indicators. Simulations conducted using the R language show that the use of Gaussian kernel estimation to estimate an income density function results in a strongly biased variance estimate. We are proposing two other density estimation methods that significantly reduce the observed bias. One of the methods has already been outlined by Deville (2000). The results published in this article will help to significantly improve the quality of information on the precision of certain Laeken indicators that are disseminated and compared internationally.

Keywords: influence function; EU-SILC survey; non-linear statistics; poverty and inequality indicators.

Table of content

• 1 Introduction
• 2 Review of given poverty indicators and their linearized variables
• 3 Estimating the income density function
• 4 Results
• 5 Conclusions
• Acknowledgments
• References

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Notes

1. Eric Graf and Yves Tillé, Institute of Statistics, Faculty of Economics and Business, University of Neuchâtel, Rue de la Pierre-à-Mazel 7, 2000 Neuchâtel, Switzerland. Email: eric.graf@unine.ch and yves.tille@unine.ch.