Asymptotic normality for deconvolution kernel density estimators

Jianqing Fan

Statistics Theory and Methods mathscidoc:1912.43286

Sankhy: The Indian Journal of Statistics, Series A, 97-110, 1991.2
Suppose that we have n observations from the convolution model Y = X+, where X and are the independent unobservable random variables, and is measurement error with a known distribution. We will discuss the asymptotic normality for deconvolving kernel density estimators of the unknown density f_{X}(.) of X by assuming either the tail of the characteristic function of behaves as f_{X}(.) (which is called supersmooth error), or the tail of the characteristic function is of order f_{X}(.) (called ordinary smooth error). Asymptotic normality of estimating the functional f_{X}(.) is also addressed.
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@inproceedings{jianqing1991asymptotic,
  title={Asymptotic normality for deconvolution kernel density estimators},
  author={Jianqing Fan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113506696827846},
  booktitle={Sankhy: The Indian Journal of Statistics, Series A},
  pages={97-110},
  year={1991},
}
Jianqing Fan. Asymptotic normality for deconvolution kernel density estimators. 1991. In Sankhy: The Indian Journal of Statistics, Series A. pp.97-110. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113506696827846.
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