Design-based estimation for geometric quantiles with application to outlier detection
AbstractGeometric 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 54 (2010)
Issue (Month): 10 (October)
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Web page: http://www.elsevier.com/locate/csda
Bahadur expansion Consistent estimator Estimating equation Horvitz-Thompson estimator Newton-Raphson iterative methods Quantile contour plot Variance estimation;
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