다변량 분산분석에서 개선된 비모수적 붓스트랩 방법 (Modified Nonparametric Bootstrap Method in MANOVA)

서지정보

· 발행기관 : 한국설비안전학회
· 수록지 정보 : 한국설비안전학회지 / 22권 / 4호 / 87 ~ 93페이지
· 저자명 : 유기상, 진서훈

초록

In general, MANOVA that verifies the relationship between two or more continuous dependent variables and categorical independent variables is possible when the assumption of multivariate normality, equal variances, and sphericity assumption. However, most of the actual data that can be obtained, especially a small number of sample data are difficult to meet the above assumptions. Therefore, since the results of the analysis by the parametric method are difficult to be relied upon, mainly the bootstrap method has been studied as a nonparametric approach. Konietschke et al.[3] presented a parametric and nonparametric bootstrap method that can be used in small sample sizes that do not satisfy the assumptions of multivariate normality and equal variances. However, due to the resampling method which ignores treatment groups, there is a problem that the bootstrap distribution of test statistic under the null hypothesis is different from the theoretically approximated distribution when null hypotheses is untrue. In order to solve these problems, we propose a nonparametric bootstrap method that resamples residuals from each treatment group. The proposed method shows that even if the null hypothesis is not satisfied, theoretically approximated distribution and bootstrap distribution are similar. We also confirmed that the results of the proposed method are improved over the existing methods through the example data.

영어초록

In general, MANOVA that verifies the relationship between two or more continuous dependent variables and categorical independent variables is possible when the assumption of multivariate normality, equal variances, and sphericity assumption. However, most of the actual data that can be obtained, especially a small number of sample data are difficult to meet the above assumptions. Therefore, since the results of the analysis by the parametric method are difficult to be relied upon, mainly the bootstrap method has been studied as a nonparametric approach. Konietschke et al.[3] presented a parametric and nonparametric bootstrap method that can be used in small sample sizes that do not satisfy the assumptions of multivariate normality and equal variances. However, due to the resampling method which ignores treatment groups, there is a problem that the bootstrap distribution of test statistic under the null hypothesis is different from the theoretically approximated distribution when null hypotheses is untrue. In order to solve these problems, we propose a nonparametric bootstrap method that resamples residuals from each treatment group. The proposed method shows that even if the null hypothesis is not satisfied, theoretically approximated distribution and bootstrap distribution are similar. We also confirmed that the results of the proposed method are improved over the existing methods through the example data.

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