当前位置: X-MOL 学术J. Stat. Comput. Simul. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Exact distribution of the F-statistic under heteroskedasticity of unknown form for improved inference
Journal of Statistical Computation and Simulation ( IF 1.2 ) Pub Date : 2021-01-14 , DOI: 10.1080/00949655.2020.1871480
Jianghao Chu 1 , Tae-Hwy Lee 1 , Aman Ullah 1 , Haifeng Xu 2
Affiliation  

In this paper, we derive the exact finite sample distribution of the F (=t2) statistic for a single linear restriction on the regression parameters. We show that the F statistic can be expressed as a ratio of quadratic forms, and therefore its exact cumulative distribution under the null hypothesis can be derived from the result of Imhof [Computing the distribution of quadratic forms in normal variables. Biometrika. 1961;48(3/4):419–426]. A numerical calculation is carried out for the exact distribution of the F statistic using various HC covariance matrix estimators, and the rejection probability under the null hypothesis (size) based on the exact distribution is examined. The results show the exact finite sample distribution is remarkably reliable, while, in comparison, the use of the F-table leads to a serious over-rejection when the sample is not large or leveraged/unbalanced.



中文翻译:

未知形式异方差下 F 统计量的精确分布以改进推理

在本文中,我们推导出F (=2) 对回归参数的单个线性限制的统计量。我们表明F统计量可以表示为二次形式的比率,因此它在原假设下的确切累积分布可以从 Imhof [计算正态变量中二次形式的分布。生物识别。1961;48(3/4):419–426]。使用各种 HC 协方差矩阵估计器对F统计量的精确分布进行数值计算,并检查基于精确分布的原假设(大小)下的拒绝概率。结果表明精确的有限样本分布非常可靠,而相比之下,使用F-table 当样本不大或杠杆/不平衡时会导致严重的过度拒绝。

更新日期:2021-01-14
down
wechat
bug