High-Order Conditional Quantile Estimation Based on Nonparametric Models of Regression
提出一种在非参数回归模型中估计高阶条件分位数的方法，基于极值理论和残差极大似然估计，适用于金融条件风险价值估计等领域。
We consider the estimation of a high order quantile associated with the conditional distribution of a regressand in a nonparametric regression model. Our estimator is inspired by Pickands (1975 Pickands , J. ( 1975 ). Statistical inference using extreme order statistics . Annals of Statistics 3 : 119 – 131 .[Crossref], [Web of Science ®] , [Google Scholar]) where it is shown that arbitrary distributions which lie in the domain of attraction of an extreme value type have tails that, in the limit, behave as generalized Pareto distributions (GPD). Smith (1987 Smith , R. L. ( 1987 ). Estimating tails of probability distributions . Annals of Statistics 15 : 1174 – 1207 .[Crossref], [Web of Science ®] , [Google Scholar]) has studied the asymptotic properties of maximum likelihood (ML) estimators for the parameters of the GPD in this context, but in our paper the relevant random variables used in estimation are standardized residuals from a first stage kernel based nonparametric estimation. We obtain convergence in probability and distribution of the residual based ML estimator for the parameters of the GPD as well as the asymptotic distribution for a suitably defined quantile estimator. A Monte Carlo study provides evidence that our estimator behaves well in finite samples and is easily implementable. Our results have direct application in finance, particularly in the estimation of conditional Value-at-Risk, but other researchers in applied fields such as insurance will also find the results useful.