On the multivariate asymptotic distribution of sequential Chi-square statistics

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-squaredifference tests are asymptotically independent. Some Monte Carlo evidence on the applicability of the theory is provided.This research was carried out while the first author was Visiting Professor in the Department of Statistics in the University of South Africa, and was supported in part by a research grant (NSERC #67-4640) from the National Sciences and Engineering Council of Canada to the first author. The support of both of these organizations is acknowledged with gratitude.