  We derive estimates for the largest and smallest singular values of sparse
rectangular $N\times n$ random matrices, assuming $\lim_{N,n\to\infty}\frac
nN=y\in(0,1)$. We consider a model with sparsity parameter $p_N$ such that
$Np_N\sim \log^{\alpha }N$ for some $\alpha>1$, and assume that the moments of
the matrix elements satisfy the condition $\mathbf E|X_{jk}|^{4+\delta}\le
C<\infty$. We assume also that the entries of matrices we consider are
truncated at the level $(Np_N)^{\frac12-\varkappa}$ with
$\varkappa:=\frac{\delta}{2(4+\delta)}$.
