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Robust modified classical spherical tests in the presence of outliers
Statistical Papers ( IF 1.3 ) Pub Date : 2022-01-25 , DOI: 10.1007/s00362-022-01289-w
Laíla Luana Campos 1 , Daniel Furtado Ferreira 1
Affiliation  

This paper verifies if the classical test to sphericity hypotheses with homogeneous variances equal to one and null covariances is applicable for cases in the presence of outliers based on four different tests performed to verify its robustness. The classical likelihood ratio test (LTR) is applied and we also propose some of its modifications in wich the sample covariance matrix is switched by one of its robust estimators, and since there is an assumption violation due to the presence of outliers, a Monte Carlo version of both asymptotic versions is considered. The normal and contaminated normal distributions are also considered. In conclusion, two of the tests are robust in the presence of outliers in a multivariate normal distribution: the Monte Carlo version of the original test (LRTMC) and the Monte Carlo version of the modified test where the sample covariance matrix is switched by the comedian estimator (LRTMCR), and the most powerful test is LRTMC.



中文翻译:

存在异常值时的稳健修正经典球面检验

本文验证了对均匀方差等于 1 和零协方差的球形假设的经典测试是否适用于存在异常值的情况,基于执行的四种不同测试来验证其稳健性。应用了经典似然比检验 (LTR),我们还提出了一些修改,其中样本协方差矩阵由其稳健的估计器之一切换,并且由于存在异常值而违反假设,蒙特卡洛考虑两个渐近版本的版本。还考虑了正态分布和污染正态分布。总之,在多元正态分布中存在异常值的情况下,其中两个检验是稳健的:

更新日期:2022-01-25
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