General Estimating Equations: Model Selection and Estimation with Diverging Number of Parameters

This paper develops adaptive elastic net estimator for general estimating equations. We allow for number of parameters diverge to infinity. The estimator can also handle collinearity among large number of variables as well. This method has the oracle property, meaning we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. This paper generalizes the least squares based adaptive elastic net estimator of Zou and Zhang (2009) to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators lack of closed form solution.