A "curse of dimensionality" arises when one tries to use the GMM based on a continuum of moments conditions to estimate a high dimensional multivariate model. The solution proposed consists of converting the high dimensional model into a continuum of auxiliary univariate models. An indirect continuum estimator is obtained as an optimal weighted average of the solutions to the univariate models. The optimal weighting function is derived and the asymptotic properties of the resulting estimators are examined. An implementation strategy is proposed and illustrated with two simulation studies and an empirical application based on an Autogressive Variance Gamma model.