无交叉多指标分位数回归模型中的估计与推断

Estimation and inference for non-crossing multiple-index quantile regression

在过去的30年中分位数回归模型的研究已十分深入.然而在实际的应用场景中,由传统估计方法所得到的分位数回归估计量,经常会在不同分位数水平上出现互相交叉的现象,这给分位数回归模型的实际应用造成了解释和预测上的困难.为解决这个问题,本文提出一种带单调约束的半参数多指标分位数回归模型的研究框架.首先将半参数多指标分位数回归模型与充分降维模型相结合,并利用两者间的联系获得指标估计量的相合估计.之后使用张量积样条方法拟合半参数模型在单调约束条件下的非参数结构.通过数值模拟的方式比较所提方法与现有可行方案所得结果在平均预测误差上的差异,实验结果和实际案例的结果都验证了本文所提出模型的可行性.

Though the theoretical properties of quantile regression have been extensively studied in the past three decades, in practice it is not unusual to obtain crossing surfaces by estimating regression functions at different quantile levels with regular approaches. The crossing quantile surfaces are intrinsically uninterpretable.To address this issue, we consider the semiparametric multi-index quantile regression subject to the monotonicity restriction at different quantile levels. We first connect the semiparametric multi-index quantile regression with a dimension-reducible model. Such a relationship allows us to estimate the index coefficients consistently. The B-splines are then used to approximate the nonparametric function under the monotonicity restriction, which numerically corresponds to a constrained linear programming problem. To further improve the efficiency, we estimate the B-spline coefficients based on the dual of the constrained optimization problem. We assess the finite-sample performance of our proposed method through a comprehensive simulation study, and compare the prediction performance of different methods through a real case study.