  Let $(\acute{N},g,\nabla )$\ be a $2n$-dimensional quasi-statistical manifold
that admits a pseudo-Riemannian metric $g$ (or $h)$ and a linear connection
$\nabla $ with torsion. This paper aims to study an almost Hermitian structure
$(g,L)$ and an almost anti-Hermitian structure $(h,L)$ on a quasi-statistical
manifold that admit an almost complex structure $L$. Firstly, under certain
conditions, we present the integrability of the almost complex structure $L$.
We show that when $d^\nabla L =0$ and the condition of torsion-compatibility
are satisfied, $(\acute{N},g,\nabla ,$ $L)$ turns into a K\"{a}hler manifold.
Secondly, we give necessary and sufficient conditions under which
$(\acute{N},h,\nabla ,L)$ is an anti-K\"{a}% hler manifold, where $h$ is an
anti-Hermitian metric. Moreover, we search the necessary conditions for
$(\acute{N},h,\nabla ,L)$ to be a quasi-K\"{a}hler-Norden manifold.
