Yebin Cheng () (Faculty of Economics and Econometrics, Universiteit van Amsterdam) Jan G. de Gooijer () (Faculty of Economics and Econometrics, Universiteit van Amsterdam)
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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.
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Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
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