Geodesic
Asymptotic minimaxity of chi-square tests
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 668-695

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We consider the asymptotic behavior of chi-square tests when a number $k_n$ of cells increases as the sample size $n$ grows. For such a setting we show that a sequence of chi-square tests is asymptotically minimax if $k_n = o(n^2)$ as $n \to \infty$. The proof makes use of a theorem about asymptotic normality of chi-square test statistics obtained under new assumptions.
Keywords: chi-square tests, asymptotic efficiency, asymptotic normality, asymptotically minimax approach, goodness-of-fit testing. 
@article{TVP_1997_42_4_a1,
     author = {M. S. Ermakov},
     title = {Asymptotic minimaxity of chi-square tests},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {668--695},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a1/}
}
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M. S. Ermakov. Asymptotic minimaxity of chi-square tests. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 668-695. http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a1/