The weight matrix in asymptotic distribution-free methods
The weight matrix in asymptotic distribution-free methods
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渐进无分布方法中的权重矩阵
DOI：
10.1111/j.2044-8317.1985.tb00833.x
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发表时间：
1985
影响因子：
2.6
通讯作者：
P. Bentler
中科院分区：
文献类型：
--
作者：
A. Mooijaart;P. Bentler
无渐近分布(ADF)方法的一个重要问题是权重矩阵的大小。然而，在观测变量为正态分布的假设下，权矩阵可以很好地分解为两个较小阶的矩阵，而在非正态分布下，这不能直接完成。本文提出了一种将权重矩阵分解为低阶矩阵的方法，使得求逆矩阵的计算量更小，并将ADF方法的应用扩展到变量数较多的应用领域。
我们方法的另一个优点是权重矩阵是根据模型参数来表示的。因此，人们应该期待权重矩阵比根据数据本身计算权重矩阵的情况更稳定。此外，参数估计的偏差可能较小，这是ADF方法中经常出现的问题。
An important problem with asymptotic distribution-free (ADF) methods is the size of the weight matrix. Whereas under the assumption of normality of the observed variables the weight matrix can nicely be decomposed into two matrices of smaller order, under non-normality this cannot be done straightforwardly. In this paper we propose a method in which the weight matrix can be decomposed into matrices of smaller order, which makes inverting the matrix computationally less heavy and extends the usefulness of ADF methods to applications with a larger number of variables.
An additional advantage of our method is that the weight matrix is formulated in terms of model parameters. As a consequence, one should expect the weight matrix to be more stable than in cases in which the weight matrix is computed from the data itself. In addition, estimates of the parameters may be less biased, a problem which often arises in ADF methods.