Nonparametric Regression with Errors in Variables

作者：Jianqing Fan, Young Kinh-Nhue Truong · 发表于：The Annals of Statistics · 年份：1993 · DOI：10.1214/aos/1176349402 · 被引用次数：336 · 研究领域：Statistical Methods and Inference、Statistical Methods and Bayesian Inference、Advanced Statistical Methods and Models

The effect of errors in variables in nonparametric regression estimation is examined. To account for errors in covariates, deconvolution is involved in the construction of a new class of kernel estimators. It is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution. In fact, there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth. It is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate, which is rich enough for many practical applications. Furthermore, to achieve optimality, we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators.