Generalized moment based estimation and inference

In this paper we consider the case of the general linear statistical model, where the stochastic design matrix has the property that its expectation and probability limits with the vector of unobserved disturbances does not equal to a zero vector and moreover, the explanatory and/or instrumental variables are ill-conditioned. In this context, we contemplate generalized moment based estimating functions that may be biased, and for which the corresponding system of moment conditions are overdetermined. To cope with this situation, we propose a new estimator with attractive finite and asymptotic sampling properties and that result in entropic densities on model parameters.