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

Mohamed Chaouch and Camelia Goga

Computational Statistics & Data Analysis, 2010, vol. 54, issue 10, 2214-2229

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.

Keywords: Bahadur; expansion; Consistent; estimator; Estimating; equation; Horvitz-Thompson; estimator; Newton-Raphson; iterative; methods; Quantile; contour; plot; Variance; estimation (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:54:y:2010:i:10:p:2214-2229

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