  This paper presents a weighted optimization framework that unifies the
binary,multi-valued, continuous, as well as mixture of discrete and continuous
treatment, under the unconfounded treatment assignment. With a general loss
function, the framework includes the average, quantile and asymmetric least
squares causal effect of treatment as special cases. For this general
framework, we first derive the semiparametric efficiency bound for the causal
effect of treatment, extending the existing bound results to a wider class of
models. We then propose a generalized optimization estimation for the causal
effect with weights estimated by solving an expanding set of equations. Under
some sufficient conditions, we establish consistency and asymptotic normality
of the proposed estimator of the causal effect and show that the estimator
attains our semiparametric efficiency bound, thereby extending the existing
literature on efficient estimation of causal effect to a wider class of
applications. Finally, we discuss etimation of some causal effect functionals
such as the treatment effect curve and the average outcome. To evaluate the
finite sample performance of the proposed procedure, we conduct a small scale
simulation study and find that the proposed estimation has practical value. To
illustrate the applicability of the procedure, we revisit the literature on
campaign advertise and campaign contributions. Unlike the existing procedures
which produce mixed results, we find no evidence of campaign advertise on
campaign contribution.
