Asymptotic minimaxity of chi-square tests

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 --> infinity. The proof makes use of a theorem about asymptotic normality of chi-square test statistics obtained under new assumptions.