Two simple approximations to the distributions of quadratic forms.
Two simple approximations to the distributions of quadratic forms.
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DOI：
10.1348/000711009x449771
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发表时间：
2010-05
期刊：
影响因子：
--
通讯作者：
Bentler PM
中科院分区：
文献类型：
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作者：
Yuan KH;Bentler PM
许多检验统计量渐近等价于正态变量的二次形式，进一步等价于 zi 独立且遵循 N(0, 1)。 T 分布的两种近似值已在流行软件中实现，并广泛用于评估各种模型。重要的是要知道这些近似值相互比较以及与 T 的精确分布相比有多准确。本文系统地研究了这两个近似值的质量，并通过分析和蒙特卡罗检验了 λi 和自由度 d 的影响。结果表明，调整后的 T 分布与了解其精确分布一样好。当 λi 的变异系数较小时，重新调整的统计量也足以用于实际模型推理。但是，当 λi 之间存在显着差异时，特别是当 d 也很大时，比较 TR 会夸大 I 类错误。
Many test statistics are asymptotically equivalent to quadratic forms of normal variables, which are further equivalent to with zi being independent and following N(0, 1). Two approximations to the distribution of T have been implemented in popular software and are widely used in evaluating various models. It is important to know how accurate these approximations are when compared to each other and to the exact distribution of T. The paper systematically studies the quality of the two approximations and examines the effect of λi's and the degrees of freedom d by analysis and Monte Carlo. The results imply that the adjusted distribution for T can be as good as knowing its exact distribution. When the coefficient of variation of the λi's is small, the rescaled statistic is also adequate for practical model inference. But comparing TR against will inflate type I errors when substantial differences exist among the λi's, especially, when d is also large.