$\frac{1}{n-{\mathcal{l}}_n}{\displaystyle \sum _{j={\mathcal{l}}_n}^{n-1}\frac{{\widehat{\text{Rem}}}_{nj}}{{\widehat{\sigma }}_{nj}}\lesssim \frac{{\gamma }^{-1/2}{\delta }^{-5/2}}{n-{\mathcal{l}}_n}{\displaystyle \sum _{j={\mathcal{l}}_n}^{n-1}{(K_{nj})}^{20}}}$	(Lemmas A.7, A.8, and A.9)
$=\frac{{\gamma }^{-1/2}{\delta }^{-5/2}}{n-{\mathcal{l}}_n}\log \max \{n,p\}{\displaystyle \sum _{j={\mathcal{l}}_n}^{n-1}{j}^{-1}}$	(Eq. A.5)
$\lesssim \frac{{\gamma }^{-1/2}{\delta }^{-5/2}}{n-{\mathcal{l}}_n}\log \max \{n.p\}\log \frac{n}{{\mathcal{l}}_n}$	$$({\sum }_a^b{j}^{-1}\le {\displaystyle {\int }_{a-1}^b{j}^{-1}dj})$$
$=o\left({[n-{\mathcal{l}}_n]}^{-1/2}\right).$	(Eqs. A.7 and A.8)