离群值剔除后的Behrens-Fisher问题推断*

doi:10.7523/j.ucas.2025.018

摘要/Abstract

摘要： 选择推断旨在修正采用 “检测-遗忘 ”策略处理异常值对统计推断所造成的偏差。在本文中,我们研究了经典的Behrens-Fisher问题。在数据含有异常值时,利用选择推断修正了传统的Welch区间和基于广义枢轴量的置信区间,给出了若干异方差下两正态总体均值差的新置信区间。通过蒙特卡罗模拟和实际数据分析比较了这些方法,对实际应用给出了参考。

关键词: 选择推断, 广义枢轴量, 截尾分布

Abstract: Selective inference aims at reducing the bias caused by the detect-and-forget strategy for handling statistical inferential problems in the presence of outliers. In this paper, we study selective inference for the classical Behrens-Fisher problem. Several selective confidence intervals for the difference between the means of two normal populations with unequal variances are presented, including the selective modifications of the traditional Welch’s interval and several generalized pivotal quantities-based intervals. These methods are compared via Monte Carlo simulations and a real data analysis. Suggestions for practical use are also discussed.

Key words: selective inference, generalized pivotal quantity, truncated distribution

中图分类号:

O212.7

牟唯嫣, 汪俊豪, 熊世峰. 离群值剔除后的Behrens-Fisher问题推断^*[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2025.018.

MU Weiyan, WANG Junhao, XIONG Shifeng. Inference for the Behrens-Fisher problem after outlier removal[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2025.018.

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离群值剔除后的Behrens-Fisher问题推断^*

Inference for the Behrens-Fisher problem after outlier removal

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[1]	牟唯嫣, 贾晓芳, 熊世峰. 逆瑞利分布和对数逻辑分布下过程能力指数的区间估计[J]. 中国科学院大学学报, 2024, 41(6): 728-735.
[2]	牟唯嫣,熊世峰. 混合模型中的广义置信域[J]. 中国科学院大学学报, 2008, 25(3): 297-304.
[3]	扈慧敏　杨荣　徐兴忠. 单因素方差分析模型中的广义p-值[J]. 中国科学院大学学报, 2007, 24(4): 408-418.