Before revision:  A standard approach is to reduce the problem to a finite set of marginal moment conditions and apply the optimally weighted generalized method of moments (OWGMM), but this requires we know a finite set of identifying moments, can still be inefficient even if identifying, or can be unwieldy and impractical if we use a growing sieve of moments .
After revision:  A standard approach is to reduce the problem to a finite set of marginal moment conditions and apply the optimally weighted generalized method of moments (OWGMM), but this requires we know a finite set of identifying moments, can still be inefficient even if identifying, or can be theoretically efficient but practically unwieldy if we use a growing sieve of moments .