6533b7ddfe1ef96bd12746f2

RESEARCH PRODUCT

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

Camelia GogaMohamed Chaouch

subject

Statistics and ProbabilityStatistics::TheoryTheoryofComputation_COMPUTATIONBYABSTRACTDEVICESStatistics::ApplicationsComputingMethodologies_SIMULATIONANDMODELINGApplied MathematicsMathematicsofComputing_NUMERICALANALYSISUnivariateInformationSystems_DATABASEMANAGEMENTEstimatorStatistics::ComputationQuantile regressionHorvitz–Thompson estimatorComputational MathematicsDelta methodComputational Theory and MathematicsTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYOutlierConsistent estimatorStatisticsStatistics::MethodologyMathematicsQuantile

description

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.

yearjournalcountryeditionlanguage
2010-10-01Computational Statistics & Data Analysis
https://doi.org/10.1016/j.csda.2010.03.006