• 论文 •

### 基于线性模型平均估计的置信区间

1. 北京中医药大学中药学院, 北京 100102;中国科学院大学数 学科学学院,北京 100049; 中国科学院数学与系统科学研究院,北京 100190
• 出版日期:2020-10-25 发布日期:2020-11-16

WANG Miaomiao. Confidence Interval Based on Model Average Estimator for Linear Regression[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(10): 1866-1881.

### Confidence Interval Based on Model Average Estimator for Linear Regression

WANG Miaomiao

1. School of Chinese Materia Medica, Beijing University of Chinese Medicine, Beijing 100102; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049; Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190
• Online:2020-10-25 Published:2020-11-16

Most investigations on statistical inferences based on model averaging estimators have been conducted under the local misspecification assumption. Hjort and Claeskens (2003) is one of the most famous articles. However, although the local misspecification assumption provides a suitable framework for studying the asymptotic properties of frequentist model averaging estimators, Raftery and Zheng (2003) have raised doubts and explanations for this assumption. In this paper, we study the confidence interval estimation methods in Hjort and Claeskens (2003). It is proved that under general fixed parameter setup, although the asymptotic distribution theory in Hjort and Claeskens (2003) is not necessarily true, the confidence interval construction method for linear functions of uncertain parameters is still asymptotically valid in linear regression with normally distributed error. This means that the coverage probability of the confidence interval tends to the nominal level. Our simulation results support the theoretical conclusion.

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