Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces
提出一种新参数化方法，用无约束标量、向量和函数参数刻画任意凸预测域上的非交叉分位平面，结合高斯过程先验和MCMC实现联合估计，在精度和模型拟合上优于现有方法。
In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parameterization that characterizes any collection of noncrossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar, vector and function valued parameters. Statistical models based on this parameterization inherit a fast computation of the likelihood function, enabling penalized likelihood or Bayesian approaches to model fitting. We introduce a complete Bayesian methodology by using Gaussian process prior distributions on the function valued parameters and develop a robust and efficient Markov chain Monte Carlo parameter estimation. The resulting method is shown to offer posterior consistency under mild tail and regularity conditions. We present several illustrative examples where the new method is compared against existing approaches and is found to offer better accuracy, coverage and model fit. Supplementary materials for this article are available online.