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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 54 (2010)
Issue (Month): 10 (October)
Contact details of provider:
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;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Unnikrishnan, N.K., 2010. "Bayesian analysis for outliers in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1962-1974, August.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Biman Chakraborty, 2001. "On Affine Equivariant Multivariate Quantiles," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(2), pages 380-403, June.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.