On Estimating Quantiles Using Auxiliary Information
Yves G. Berger¹, Juan F. Muñoz²
¹Southampton Statistical Sciences Research Institute, University of Southampton, Southampton, England, United Kingdom; ²Department of Quantitative Methods in Economics and Business, University of Granada, Granada, Andalucia, Spain

Estimation of quantiles may be of considerable interest when measuring income distribution and poverty lines. For instance, the median is regarded as a more appropriate measure of location than the mean when variables, such as income, expenditure, etc, exhibit highly skewed distributions. In sample surveys, auxiliary information is often used at the estimation stage to increase the precision of estimators of means. The use of auxiliary information has been studied extensively for estimation of means, but it has no obvious extensions to the estimation of quantiles. A novel method for estimating quantiles using auxiliary information is proposed. The proposed estimator is based upon the regression estimator of a transformation of the variable of interest. Simulation studies support our finding and show that the proposed estimator can be more accurate than or as accurate as alternative estimators (Chambers & Dunstan, 1986; Rao et al. 1990; Silva & Skinner 1995) which can be computationally more intensive.

Chambers, R. L. & Dunstan, R. (1986). Estimating distribution functions from survey data. Biometrika 73, 597-604.

Rao, J. N. K., Kovar, J. G. & Mantel, H. J. (1990). On estimating distribution functions and quantiles from survey

Silva, P. L. D. & Skinner, C. J. (1995). Estimating distribution functions with auxiliary information using poststratification. J. Offic. Statist. 11, 277-94.

Résumé: Nous proposons une nouvelle approche pour estimer un quantile. Cette approche utilise l'information auxiliaire et est basée sur une transformation de la variable d'intérêt. Nous présenterons également quelques résultats de simulation.

Keywords: Distribution Function; Horvitz-Thompson estimator; Regression Estimator; Sample Surveys

Biography: Yves Berger has established a world-class research program and body of work in important and related issues fundamental to efficient and valid statistical inference from complex sample surveys. These include: variance estimation under complex sampling involving unequal probabilities; repeated surveys; non-response; imputation; and adaptive sampling. A distinctive feature of Yves Berger's research program is that it tackles fundamental theoretical issues that result in practical applications.