无交叉多指标分位数回归模型中的估计与推断

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...

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

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.