Nonparametric Multivariate Conditional Distribution and Quantile Regression

27 Pages Posted: 10 Sep 2008

See all articles by Keming Yu

Keming Yu

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications

Xiaochen (Michael) Sun

HSBC Global Asset Management

Gautam Mitra

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications

Date Written: September 1, 2008

Abstract

In nonparametric multivariate regression analysis, one usually seeks methods to reduce the dimensionality of the regression function to bypass the difficulty caused by the curse of dimensionality. We study nonparametric estimation of multivariate conditional distribution and quantile regression via local univariate quadratic estimation of partial derivatives of bivariate copulas. Without restricting the form of underlying regression function or using dimensional reduction, we show that a d-dimensional multivariate conditional distribution and quantile regression could be estimated by d(d 1)/2 times of univariate smoothers. The asymptotic bias and variance as well as smoothing parameter selection method are derived. Simulations show that the method works quite well. The techniques are illustrated by application to exchange rate data.

Keywords: Conditional distribution, Conditional quantiles, Copula, High-dimension, Local quadratic regression, nonparametric estimation, Partial derivative, Semiparametric estimation

Suggested Citation

Yu, Keming and Sun, Xiaochen (Michael) and Mitra, Gautam, Nonparametric Multivariate Conditional Distribution and Quantile Regression (September 1, 2008). Available at SSRN: https://ssrn.com/abstract=1264946 or http://dx.doi.org/10.2139/ssrn.1264946

Keming Yu

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications

John Crank Building
Brunel University
Uxbridge, UB8 3PH
United Kingdom

Xiaochen (Michael) Sun (Contact Author)

HSBC Global Asset Management ( email )

78 St. James's Street
London, London SW1A 1EJ
United Kingdom

Gautam Mitra

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications ( email )

John Crank Building
Brunel University
Uxbridge, UB8 3PH
United Kingdom

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