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

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 setups. An algorithm to compute 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. Key words: Bahadur expansion; consistent estimator; estimating equation; Horvitz-Thompson estimator; Newton-Raphson iterative methods; quantile contour plot; variance estimation.

• Type: Journal
• Year: 2010
• Where: CSDA
• Authors: Mohamed Chaouch, Camelia Goga
• Keywords: CSDA 2010, Geometric Quantile, Multivariate, Quantile