Nonparametric estimation of quadratic regression functionals

Li-Shan Huang Jianqing Fan

Statistics Theory and Methods mathscidoc:1912.43354

Bernoulli, 5, (5), 927-949, 1999
Quadratic regression functionals are important for bandwidth selection of nonparametric regression techniques and for nonparametric goodness-of-fit test. Based on local polynomial regression, we propose estimators for weighted integrals of squared derivatives of regression functions. The rates of convergence in mean square error are calculated under various degrees of smoothness and appropriate values of the smoothing parameter. Asymptotic distributions of the proposed quadratic estimators are considered with the Gaussian noise assumption. It is shown that when the estimators are pseudo-quadratic (linear components dominate quadratic components), asymptotic normality with rate n-1/2 can be achieved.
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@inproceedings{li-shan1999nonparametric,
  title={Nonparametric estimation of quadratic regression functionals},
  author={Li-Shan Huang, and Jianqing Fan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113910791268914},
  booktitle={Bernoulli},
  volume={5},
  number={5},
  pages={927-949},
  year={1999},
}
Li-Shan Huang, and Jianqing Fan. Nonparametric estimation of quadratic regression functionals. 1999. Vol. 5. In Bernoulli. pp.927-949. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113910791268914.
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