Geodesic
A family of multivariate chi-square statistics
Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 130-142.

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We consider a sequence of independent trials, which, under the hypothesis $H_0$, 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 $H_0$ and the alternatives contigual to $H_0$. 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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B. I. Selivanov. A family of multivariate chi-square statistics. Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 130-142. http://geodesic.mathdoc.fr/item/DM_2002_14_3_a12/

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