Abstract
Abstract We consider a sequence of independent trials, which, under the hypothesis H0, is a realisation of some polynomial scheme. We define a family of multivariate chi-square statistics which includes the sequential chi-square test statistics. We formulate conditions which guarantee that the distributions of the statistics under consideration converge to limit distributions under the hypothesis H0 and the alternatives contigual to H0. We find the form of the Laplace transforms of the limit distributions of the statistics of the family. This research was supported by the Russian Foundation for Basic Research, grant 00-15-96136.
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