  This paper presents a novel generic asymptotic expansion formula of
expectations of multidimensional Wiener functionals through a Malliavin
calculus technique. The uniform estimate of the asymptotic expansion is shown
under a weaker condition on the Malliavin covariance matrix of the target
Wiener functional. In particular, the method provides a tractable expansion for
the expectation of an irregular functional of the solution to a
multidimensional rough differential equation driven by fractional Brownian
motion with Hurst index $H<1/2$, without using complicated fractional integral
calculus for the singular kernel. In a numerical experiment, our expansion
shows a much better approximation for a probability distribution function than
its normal approximation, which demonstrates the validity of the proposed
method.
