  This paper considers estimation and inference in semiparametric econometric
models. Standard procedures estimate the model based on an independence
restriction that induces a minimum distance between a joint cumulative
distribution function and the product of the marginal cumulative distribution
functions. This paper develops a new estimator which generalizes estimation by
allowing endogeneity of the weighting measure and estimating the optimal
measure nonparametrically. The optimality corresponds to the minimum of the
integrated distance. To accomplish this aim we use Kantorovich's formulation of
the optimal transportation problem. The minimizing distance is equivalent to
the total variation distance and thus characterizes finer topological
structures of the distributions. The estimation also provides greater
generality by dealing with probability measures on compact metric spaces
without assuming existence of densities. Asymptotic statistics of the empirical
estimates have standard convergent results and are available for different
statistical analyses. In addition, we provide a tractable implementation for
computing the estimator in practice.
