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### 基于改进Huber损失的部分线性模型稳健经验似然推断

1. 1. 首都经济贸易大学统计学院, 北京 100070;
2. 盐城师范学院 数学与统计学院, 盐城 224002
• 收稿日期:2021-06-29 修回日期:2021-12-27 出版日期:2022-05-25 发布日期:2022-07-23
• 通讯作者: 刘强,Email:cuebliuqiang0910@126.com.
• 基金资助:
国家自然科学基金青年项目(11901508)资助课题.

SUN Huihui, LIU Qiang. Robust Orthogonal Empirical Likelihood for Partial Linear Models Based on Modified Huber's Loss Function[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(5): 1330-1343.

### Robust Orthogonal Empirical Likelihood for Partial Linear Models Based on Modified Huber's Loss Function

SUN Huihui1,2, LIU Qiang1

1. 1. School of Statistics, Capital University of Economics and Business, Beijing 100070;
2. School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002
• Received:2021-06-29 Revised:2021-12-27 Online:2022-05-25 Published:2022-07-23

This paper discusses an effective and robust empirical likelihood inference for partial linear models. The procedure applies a modified Huber's function with tail function replaced by the exponential squared loss (ESL) to achieve robustness and effectiveness. Combined with the modified Huber's loss function and QR decomposition technique, an orthogonal empirical likelihood based on Huber-ESL is proposed by improving the estimation equation in the constraint condition of empirical likelihood method to suppress the influence of outliers. Meanwhile, the parametric and nonparametric part of the models are estimated separately to avoid the mutual influence and improve the effectiveness of the estimation. Under some mild conditions, the asymptotic behavior of the robust empirical likelihood approach is established. The finite sample performance of our proposed method is studied through simulations and the proposed method is applied to the Boston house price data. The results show that the performance of our Huber-ESL based empirical likelihood method is competitive with Huber-based procedure and much better than nonrobust empirical likelihood method when the data are contaminated.

MR(2010)主题分类:

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