Open Access
September, 1951 Exact Tests of Serial Correlation using Noncircular Statistics
G. S. Watson, J. Durbin
Ann. Math. Statist. 22(3): 446-451 (September, 1951). DOI: 10.1214/aoms/1177729592


For testing the hypothesis that successive members of a series of observations are independent J. von Neumann [5] (see also B. I. Hart [4]) and R. L. Anderson [1] have proposed test statistics and tabulated their significance points. von Neumann's criterion seems well designed to detect deviations from the null hypothesis which might be encountered in practice but its exact distribution is unknown. On the other hand Anderson's statistic, while it has a known distribution, is based on a circular conception of the population which is rarely plausible in practice. In the present note certain noncircular statistics are proposed for which exact distributions can be obtained from Anderson's results. The statistics are derived from the usual noncircular statistics by sacrificing a small amount of relevant information. Their application is noted to certain regression problems for which no satisfactory tests are at present available. Finally, some general remarks are made about the choice of best statistics for the problems discussed.


Download Citation

G. S. Watson. J. Durbin. "Exact Tests of Serial Correlation using Noncircular Statistics." Ann. Math. Statist. 22 (3) 446 - 451, September, 1951.


Published: September, 1951
First available in Project Euclid: 28 April 2007

zbMATH: 0043.13904
MathSciNet: MR42663
Digital Object Identifier: 10.1214/aoms/1177729592

Rights: Copyright © 1951 Institute of Mathematical Statistics

Vol.22 • No. 3 • September, 1951
Back to Top