High dimensional data analysis using multivariate generalized spatial quantiles
High dimensional data routinely arises in image analysis, genetic experiments, network analysis, and various other research areas. Many such datasets do not correspond to well-studied probability distributions, and in several applications the data-cloud prominently displays non-symmetric and non-convex shape features. We propose using spatial quantiles and their generalizations, in particular, the projection quantile, for describing, analyzing and conducting inference with multivariate data. Minimal assumptions are made about the nature and shape characteristics of the underlying probability distribution, and we do not require the sample size to be as high as the data-dimension. We present theoretical properties of the generalized spatial quantiles, and an algorithm to compute them quickly. Our quantiles may be used to obtain multidimensional confidence or credible regions that are not required to conform to a pre-determined shape. We also propose a new notion of multidimensional order statistics, which may be used to obtain multidimensional outliers. Many of the features revealed using a generalized spatial quantile-based analysis would be missed if the data was shoehorned into a well-known probabilistic configuration.
Volume (Year): 102 (2011)
Issue (Month): 4 (April)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- Biman Chakraborty, 2001. "On Affine Equivariant Multivariate Quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 380-403, June.
- Chakraborty, Biman & Chaudhuri, Probal, 1999. "A note on the robustness of multivariate medians," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 269-276, November.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:102:y:2011:i:4:p:768-780. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.