The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper in...The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.展开更多
Currently,there is no solid criterion for judging the quality of the estimators in factor analysis.This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of fa...Currently,there is no solid criterion for judging the quality of the estimators in factor analysis.This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of factors along with the best method for factor extraction.The proposed technique consists of two steps:testing the normality of the residuals from the fitted model via the Shapiro-Wilk test and using an empirical quantified index to judge the quality of the factor model.Examples are presented to demonstrate how the method is implemented and to verify its effectiveness.展开更多
参数测量不确定度分析是动力装置性能试飞中最为关键的环节之一。当参数的概率分布不对称或者不满足正态分布时,采用SAE AIR 1678B中的平方和开方法,就可能会得到虚假的置信区间,提出将蒙特卡洛不确定评估法作为SAE AIR 1678B中方法的...参数测量不确定度分析是动力装置性能试飞中最为关键的环节之一。当参数的概率分布不对称或者不满足正态分布时,采用SAE AIR 1678B中的平方和开方法,就可能会得到虚假的置信区间,提出将蒙特卡洛不确定评估法作为SAE AIR 1678B中方法的备用方法。详细分析了性能试飞中不确定度的误差来源和处理方法,给出了蒙特卡洛法的关键技术过程,不需要计算敏感因子,并且对间接测量数据的概率分布无要求,适用性强,避免了一些传统算法的求导过程,通过算例计算,并与SAE AIR 1678B中方法的结果进行对比,结果表明此方法具有良好的工程应用价值,在实际应用中,可与SAE AIR 1678B中方法互作备份,可提高测量不确定度评价的可信度。展开更多
文摘The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.
基金Supported by the National Basic Research Program of China(2010CB126200)the National Natural Science Foundation of China(30370914)。
文摘Currently,there is no solid criterion for judging the quality of the estimators in factor analysis.This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of factors along with the best method for factor extraction.The proposed technique consists of two steps:testing the normality of the residuals from the fitted model via the Shapiro-Wilk test and using an empirical quantified index to judge the quality of the factor model.Examples are presented to demonstrate how the method is implemented and to verify its effectiveness.
文摘参数测量不确定度分析是动力装置性能试飞中最为关键的环节之一。当参数的概率分布不对称或者不满足正态分布时,采用SAE AIR 1678B中的平方和开方法,就可能会得到虚假的置信区间,提出将蒙特卡洛不确定评估法作为SAE AIR 1678B中方法的备用方法。详细分析了性能试飞中不确定度的误差来源和处理方法,给出了蒙特卡洛法的关键技术过程,不需要计算敏感因子,并且对间接测量数据的概率分布无要求,适用性强,避免了一些传统算法的求导过程,通过算例计算,并与SAE AIR 1678B中方法的结果进行对比,结果表明此方法具有良好的工程应用价值,在实际应用中,可与SAE AIR 1678B中方法互作备份,可提高测量不确定度评价的可信度。
