  We consider an estimation problem of expected functionals of a general random
element that values in a metric space. If the functional forms an explicit
function of some unknown parameters, we can estimate it by plugging-in a
suitable estimator in to the function, and we can find the asymptotic
distribution. However, if the functional is implicit in the parameters, it
causes a problem of specifying asymptotic distribution. This paper gives a
general condition to specify the asymptotic distribution even if the functional
is implicit in the parameters, and further investigates it in detail when the
random elements are semimartingales.
