  First we introduce the Bailleul-Hoshino's result [4], which links the theory
of regularity structures and the paracontrolled calculus. As an application of
their result, we give another algebraic proof of the multicomponent commutator
estimate [3], which is a generalized version of the
Gubinelli-Imkeller-Perkowski's commutator estimate [11, Lemma 2.4].
