Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/86643
Authors: 
Cheng, Yebin
de Gooijer, Jan G.
Year of Publication: 
2004
Series/Report no.: 
Tinbergen Institute Discussion Paper 04-072/4
Abstract: 
Motivated by Chaudhuri's work (1996) on unconditional geometric quantiles, we explore the asymptotic properties of sample geometric conditional quantiles, defined through kernel functions, in high dimensional spaces. We establish a Bahadur type linear representation for the geometric conditional quantile estimator and obtain the convergence rate for the corresponding remainder term. From this, asymptotic normality on the estimated geometric conditional quantile is derived. Based on these results we propose confidence ellipsoids for multivariate conditional quantiles. The methodology is illustrated via data analysis and a Monte Carlo study.
Subjects: 
Asymptotic normality
Bahadur representation
geometric conditional quantile
confidence ellipsoids
kernel function
JEL: 
C14
Document Type: 
Working Paper

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