Geodesic
A~family of multivariate $\chi^2$-statistics
Diskretnaya Matematika, Tome 16 (2004) no. 4, pp. 110-116.

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We consider a sequence of independent trials, under the hypothesis $H_0$ each of them is a realisation of a certain polynomial scheme. We introduce a family of multivariate $\chi^2$-statistics where the outcomes are equipped with weights depending on the ordinal of the trial. Earlier results on families of multivariate $\chi^2$-statistic are extended to this family. This research was supported by grant 1758.2003.1 of President of Russian Federation for support of leading scientific schools. 
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B. I. Selivanov. A~family of multivariate $\chi^2$-statistics. Diskretnaya Matematika, Tome 16 (2004) no. 4, pp. 110-116. http://geodesic.mathdoc.fr/item/DM_2004_16_4_a9/

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