Local quasi-likelihood estimation with data missing at random

Jianwei Chen Jianqing Fan Kim-Hung Li Haibo Zhou

Statistics Theory and Methods mathscidoc:1912.43345

Statistica Sinica, 16, (4), 1071, 2006.10
Local quasi-likelihood estimation is useful for nonparametric modeling in a widely-used exponential family of distributions, called generalized linear models. Yet, the technique cannot be directly applied to situations where a response variable is missing at random. Three local quasi-likelihood estimation techniques are introduced: the local quasi-likelihood estimator using only complete-data; the locally weighted quasi-likelihood method; the local quasi-likelihood estimator with imputed values. These estimators share basically the same first order asymptotic biases and variances. Our simulation results show that substantial efficiency gains can be obtained by using the local quasi-likelihood estimator with imputed values. We develop the local quasi-likelihood imputation methods for estimating the mean functional of the response variable. It is shown that the proposed mean imputation estimators are asymptotically normal with asymptotic variance that can be easily estimated. Data from an ongoing environmental epidemiologic study is used to illustrate the proposed methods.
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@inproceedings{jianwei2006local,
  title={Local quasi-likelihood estimation with data missing at random},
  author={Jianwei Chen, Jianqing Fan, Kim-Hung Li, and Haibo Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113838900310905},
  booktitle={Statistica Sinica},
  volume={16},
  number={4},
  pages={1071},
  year={2006},
}
Jianwei Chen, Jianqing Fan, Kim-Hung Li, and Haibo Zhou. Local quasi-likelihood estimation with data missing at random. 2006. Vol. 16. In Statistica Sinica. pp.1071. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113838900310905.
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