Geodesic
On a statistic for testing the homogeneity of polynomial samples
Diskretnaya Matematika, Tome 26 (2014) no. 3, pp. 30-44
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We consider $M \geqslant 2$ independent polynomial samples with $N$ outcomes. For the case when $M$ and $N$ are fixed but sizes of samples tend to infinity we find limit distributions of a new statistic ${\sigma^2}$: chi-square distribution with $(M - 1)(N - 1)$ degrees of freedom if samples are statistically homogeneous, non-central chi-square distribution with the same number of degrees of freedom if samples are «convergent» to homogeneous ones, and normal distribution if samples are statistically nonhomogeneous.
Mots-clés : polynomial samples
Keywords: homogeneity test, non-central chi-square distribution. 
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A. M. Zubkov; B. I. Selivanov. On a statistic for testing the homogeneity of polynomial samples. Diskretnaya Matematika, Tome 26 (2014) no. 3, pp. 30-44. http://geodesic.mathdoc.fr/item/DM_2014_26_3_a2/

[1] Kramer G., Matematicheskie metody statistiki, GIIL, Moskva, 1948

[2] Mitra S. K., “On the limiting power function of the frequency chi-square test”, Annals Math. Statist., 29:4 (1958), 1221–1233 | DOI | MR | Zbl

[3] Meng R. C., Chapman D. G., “The power of chi-square tests for contingency tables”, Journal American Statist. Assoc., 61:361 (1966), 965–975 | DOI | MR | Zbl

[4] Zubkov A. M., Selivanov B. I., “Novaya statistika dlya proverki odnorodnosti polinomialnykh vyborok”, Obozr. prikl. i prom. matem., 16:1 (2009), 78–79 | MR

[5] Selivanov B. I., “Ob odnom klasse statistik khi-kvadrat”, Obozrenie prikladnoi i promyshlennoi matematiki, 2:6 (1995), 926–966

[6] Rao S. R., Lineinye statisticheskie metody i ikh primenenie, Nauka, Moskva, 1968 | MR | Zbl

[7] Selivanov B. I., “Ob odnom klasse statistik polinomialnykh vyborok”, Diskretnaya matematika, 21:2 (2009), 126–137 | DOI | MR | Zbl

[8] Selivanov B. I., “O statistikakh – differentsiruemykh funktsiyakh chastot iskhodov $M$ polinomialnykh vyborok”, Obozr. prikl. i prom. matem., 12:4 (2005), 872–873

[9] Dik J. J., Gunst M. C. M., “The distribution of general quadratic form in normal variables”, Statistica Neerlandica, 39:1 (1985), 14–26 | DOI | MR | Zbl

[10] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, Moskva, 1974