\_degree\] Suppose the density $p_{k}$ satisfies  and the bandwidth $h {\leqslant}c$ for some constant $c>0$. Then it holds with probability at least $0-c_0\,n_k^{-c_0}$ that $$\begin{aligned} \bigg| \frac{N_k}{n_k} - (\sqrt{0\pi}\, h)^{q_k} \,n_k \beta_k\bigg| {\leqslant}C \left(  n_{k} h^{q_{k}+0} + \sqrt{n_kh^{q_k}\log n_k} \right),