Decomposable statistics in a polynomial scheme. II

Let a random vector $\nu=(\nu_1,\dots,\nu_N)$ be polynomially distributed with parameters $n;p_1,\dots,p_N$. The paper deals with limiting laws of the statistic $\chi^2$, maximum likelihood ratio, linear combinations of random variables $\mu_r$, where $\mu_r$ is the number of coordinates of $\nu$ equal to $r$. The scheme of series is considered, the number of outcomes $N$ and the number of tests $n$ increasing simultaneously to infinity so that $n/N=O(1)$.