Nonparametric Instrumental Variables Estimation of a Quantile Regression Model
提出一种非参数工具变量方法估计分位数回归模型，通过使工具变量条件下的分位数误差为零来识别回归函数，并证明估计量的均方相合性和最优收敛速度，蒙特卡洛实验显示有限样本表现良好。
We consider nonparametric estimation of a regression function that is identified by requiring a specified quantile of the regression "error" conditional on an instrumental variable to be zero. The resulting estimating equation is a nonlinear integral equation of the first kind, which generates an ill-posed inverse problem. The integral operator and distribution of the instrumental variable are unknown and must be estimated nonparametrically. We show that the estimator is mean-square consistent, derive its rate of convergence in probability, and give conditions under which this rate is optimal in a minimax sense. The results of Monte Carlo experiments show that the estimator behaves well in finite samples. Copyright The Econometric Society 2007.