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Title: On multivariate quantile regression
Authors: Chakraborty, B. 
Keywords: Data-driven coordinates
Multiresponse linear models
Issue Date: 15-Jan-2003
Citation: Chakraborty, B. (2003-01-15). On multivariate quantile regression. Journal of Statistical Planning and Inference 110 (1-2) : 109-132. ScholarBank@NUS Repository.
Abstract: To detect the dependence on the covariates in the lower and upper tails of the response distribution, regression quantiles are very useful tools in linear model problems with univariate response. We consider here a notion of regression quantiles for problems with multivariate responses. The approach is based on minimizing a loss function equivalent to that in the case of univariate response. To construct an a4ne equivariant notion of multivariate regression quantiles, we have considered a transformation retransformation procedure based on 'data-driven coordinate systems'. We indicate some algorithm to compute the proposed estimates and establish asymptotic normality for them. We also, suggest an adaptive procedure to select the optimal data-driven coordinate system. We discuss the performance of our estimates with the help of a 8nite sample simulation study and to illustrate our methodology, we analyzed an interesting data-set on blood pressures of a group of women and another one on the dependence of sales performances on creative test scores. © 2001 Elsevier Science B.V.
Source Title: Journal of Statistical Planning and Inference
ISSN: 03783758
Appears in Collections:Staff Publications

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