Nonparametric regression with errors in variables

Jianqing Fan Young K Truong

Statistics Theory and Methods mathscidoc:1912.43268

The Annals of Statistics, 1900-1925, 1993.12
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.
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@inproceedings{jianqing1993nonparametric,
  title={Nonparametric regression with errors in variables},
  author={Jianqing Fan, and Young K Truong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113401453890828},
  booktitle={The Annals of Statistics},
  pages={1900-1925},
  year={1993},
}
Jianqing Fan, and Young K Truong. Nonparametric regression with errors in variables. 1993. In The Annals of Statistics. pp.1900-1925. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113401453890828.
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