SOME RESULTS IN THE TESTING OF SERIAL CORRELATION COEFFICIENTS
成果类型：
Article
署名作者：
QUENOUILLE, MH
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332345
发表日期：
1948
页码：
261267
关键词：
摘要：
It had previously been shown by Rubin (1945) that the distribution of the serial coefficient, [image] with the xi normally and independently distributed about zero, is approximated by the distribution of the ordinary correlation coeff. based on n + 3 observations. Madow (1945) extended that result to obtain the distribution in the situation where the xi are connected by a linear Markoff scheme, [image] where the [epsilon]i are independently and normally distributed about zero. It is pointed out that under Fisher''s transformation, r = tanh Z, the distribution of Z is approximately normal. It is further shown by examples that the approximation remains good when the [epsilon]i are rectangularly distributed and when they take values +1 and -1 with probabili ties p and 1-p. Finally, it is suggested that the correlation between two serially correlated series is distributed approximately as the ordinary correlation coeff. provided the effective number of degrees of freedom, n[image]= n(l- [rho]1[rho]2) / (1+[rho]l [rho]2) is large.