The central limit theorem under the absence of extremal absolute order statistics

One finds conditions for the relation $\Delta_{n,r}=o(1)=\nabla_{n,r}$, где $\Delta_{n,r}=\sup_x|P\Big(\frac{S_{n,r}}{a_n}<x\Big)-\Phi(x)|$, $S_{n,r}=X_{(1)}+\dots+X_{(n-r)}$, $X_{(1)},\dots,X_{(n)}$ are the absolute order statistics for a repeated sample from a symmetric distribution.