Testing for serial correlation in least squares regression. II.
Testing for serial correlation in least squares regression. II.
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DOI：
10.1007/978-1-4612-4380-9_21
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发表时间：
1950-12
期刊：
影响因子：
2.7
通讯作者：
J. Durbin;G. Watson
中科院分区：
文献类型：
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作者：
J. Durbin;G. Watson
本文根据作者早先提出的统计量(Durbin&Watson，1950,1951)，考虑了序列相关性检验中出现的一些问题。研究了计算DARE的精确分布的方法，并对四组已发表的数据进行了DARE的精确分布与六种近似的比较。研究发现，由Theil和Nagar以及Hannan提出的近似方法对于实际应用来说是不准确的，但是在1950和1951年的论文中提出的Beta近似和我们称为Thea+Bdu近似的一种新的近似都表现得很好，就像基于d的前两个矩的Beta近似一样。从不变性理论的观点出发，将检验的能力与由Theil，Durbin，Koerts和Abrahamse提出的某些精确检验进行了比较。结果表明，D检验是局部最强不变量，而其他检验不是。有三个附录。第一个给出了d的确切分布。第二种方法将均值和方差导出为与D密切相关的修正的最大似然统计量的二阶近似。第三部分详细列出了Thea+Hudu近似所需的计算。
SUMMARYThe paper considers a number of problems arising from the test of serial correlation based on thedstatistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution ofdare investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta approximation proposed in the 1950 and 1951 papers and a new approximation, called by us thea + bduapproximation and based, like the beta approximation, on the exact first two moments ofd, both perform well.The power of thedtest is compared with that of certain exact tests proposed by Theil, Durbin, Koerts and Abrahamse from the standpoint of invariance theory. It is shown that thedtest is locally most powerful invariant but that the other tests are not.There are three appendices. The first gives an account of the exact distribution ofd. The second derives the mean and variance to a second order of approximation of a modified maximum likelihood statistic closely related tod. The third sets out details of the computations required for thea + hduapproximation.