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Design-based estimation for geometric quantiles with application to outlier detection

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  • Chaouch, Mohamed
  • Goga, Camelia

Abstract

Geometric quantiles are investigated using data collected from a complex survey. Geometric quantiles are an extension of univariate quantiles in a multivariate set-up that uses the geometry of multivariate data clouds. A very important application of geometric quantiles is the detection of outliers in multivariate data by means of quantile contours. A design-based estimator of geometric quantiles is constructed and used to compute quantile contours in order to detect outliers in both multivariate data and survey sampling set-ups. An algorithm for computing geometric quantile estimates is also developed. Under broad assumptions, the asymptotic variance of the quantile estimator is derived and a consistent variance estimator is proposed. Theoretical results are illustrated with simulated and real data.

Suggested Citation

  • Chaouch, Mohamed & Goga, Camelia, 2010. "Design-based estimation for geometric quantiles with application to outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2214-2229, October.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:10:p:2214-2229
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    References listed on IDEAS

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    1. Unnikrishnan, N.K., 2010. "Bayesian analysis for outliers in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1962-1974, August.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Biman Chakraborty, 2001. "On Affine Equivariant Multivariate Quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 380-403, June.
    4. Robert Serfling, 2002. "Quantile functions for multivariate analysis: approaches and applications," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 214-232.
    5. Anthony Y. C. Kuk & A. H. Welsh, 2001. "Robust estimation for finite populations based on a working model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 277-292.
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