Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2004-06-29
Number: 04-072/4
Author-Name: Yebin Cheng
Author-Email: y.cheng@uva.nl
Author-Workplace-Name: Faculty of Economics and Econometrics, Universiteit van Amsterdam
Author-Name: Jan G. de Gooijer
Author-Email: j.g.degooijer@uva.nl
Author-Workplace-Name: Faculty of Economics and Econometrics, Universiteit van Amsterdam
Title: On the u-th Geometric Conditional Quantile
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.
Classification-JEL: C14
Keywords: Asymptotic normality; Bahadur representation; geometric conditional quantile; confidence ellipsoids; kernel function
File-Url: https://papers.tinbergen.nl/04072.pdf
File-Format: application/pdf
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Handle: RePEc:tin:wpaper:20040072