Geodesic
Two-stage chi-square test and two-dimensional distributions of a~Bessel process
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 841-850

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We consider the sequential $r$-stage chi-square test. For $r=2$, we study the asymptotic properties of the error probabilities as a function of the sizes of the rectangular critical domain, which via the Bonferroni inequality makes it possible to derive asymptotic properties of the error probability for an arbitrary $r$. For this purpose, we obtain some properties of the Infeld function, whose derivation is of independent interest. Based on the results obtained, the asymptotic behavior of the tails of two-dimensional distributions of a Bessel process is found.
Keywords: sequential chi-square test, Bessel process. 
@article{TVP_2020_65_4_a11,
     author = {M. P. Savelov},
     title = {Two-stage chi-square test and two-dimensional distributions of {a~Bessel} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {841--850},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a11/}
}
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M. P. Savelov. Two-stage chi-square test and two-dimensional distributions of a~Bessel process. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 841-850. http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a11/