NONPARAMETRIC INSTRUMENTAL REGRESSION WITH ERRORS IN VARIABLES
针对内生变量存在经典测量误差时非参数工具变量回归估计不一致的问题，提出小波去卷积估计量，推导了不同条件下的收敛速度，并考虑了误差密度未知需估计的情形。
This paper considers nonparametric instrumental variable regression when the endogenous variable is contaminated with classical measurement error. Existing methods are inconsistent in the presence of measurement error. We propose a wavelet deconvolution estimator for the structural function that modifies the generalized Fourier coefficients of the orthogonal series estimator to take into account the measurement error. We establish the convergence rates of our estimator for the cases of mildly/severely ill-posed models and ordinary/super smooth measurement errors. We characterize how the presence of measurement error slows down the convergence rates of the estimator. We also study the case where the measurement error density is unknown and needs to be estimated, and show that the estimation error of the measurement error density is negligible under mild conditions as far as the measurement error density is symmetric.