Local quasi-likelihood with a parametric guide

Jianqing Fan Yichao Wu Yang Feng

Statistics Theory and Methods mathscidoc:1912.43352

Annals of statistics, 37, 4153, 2009.12
Generalized linear models and quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification and the resulting model is completely determined by the data themselves. However nonparametric estimation schemes generally have a slower convergence rate such as the local polynomial smoothing estimation of nonparametric generalized linear models studied in Fan, Heckman and Wand (1995). In this work, we propose two parametrically guided nonparametric estimation schemes by incorporating prior shape information on the link transformation of the response variables conditional mean in terms of the predictor variable. Asymptotic results and numerical simulations demonstrate the improvement of our new estimation schemes over the original nonparametric counterpart.
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@inproceedings{jianqing2009local,
  title={Local quasi-likelihood with a parametric guide},
  author={Jianqing Fan, Yichao Wu, and Yang Feng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113903966011912},
  booktitle={Annals of statistics},
  volume={37},
  pages={4153},
  year={2009},
}
Jianqing Fan, Yichao Wu, and Yang Feng. Local quasi-likelihood with a parametric guide. 2009. Vol. 37. In Annals of statistics. pp.4153. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113903966011912.
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