• 论文 •

### NA误差下部分线性模型的经验似然推断

1. (1)吉林大学数学学院, 长春 130012; 长春税务学院应用数学系, 长春 130117;(2)林大学数学学院, 长春 130012;(3)东北师范大学, 长春 130021.
• 收稿日期:2007-07-23 修回日期:2008-10-27 出版日期:2009-04-25 发布日期:2009-04-25

YU Zhuoxi;WANG Dehui;SHI Ningzhong. Empirical Likehood in Partial Linear Model Under NA Samples[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(4): 490-501.

### Empirical Likehood in Partial Linear Model Under NA Samples

YU Zhuoxi(1),WANG Dehui(2), SHI Ningzhong(3)

1. (1)School of Mathematics, Jilin University, Changchun 130012; Department of Mathematics, Changchun Taxation College, Changchun 130117;(2)School of Mathematics, Jilin University, Changchun 130012;(3)Northeast Normal University, Changchun 130021.
• Received:2007-07-23 Revised:2008-10-27 Online:2009-04-25 Published:2009-04-25

This paper is concerned with the typical partial linear model $y_{i}=\beta x_{i}+g(t_{i})+e_{i}, 1\leq i \leq n,$ where $(x_{i},t_{i})$ are fixed design points, $g$ is an unknown function, and $e_{i}$'s are negatively associated (NA) random errors. An empirical log-likelihood ratio for the regression coefficient is proposed, the results show that the statistic is asymptotically chi-squared distributed and that the confidence intervals can be constructed accordingly.

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