On the Existence and Information of Orthogonal Moments

Understand

Locally Robust (LR)/Orthogonal/Debiased moments have proven useful with machine learning first steps, but their existence has not been investigated for general parameters.

• In this paper, we provide a necessary and sufficient condition, referred to as Restricted Local Non-surjectivity (RLN), for the existence of such orthogonal moments to conduct robust inference on general parameters of interest in regular semiparametric models.
• Importantly, RLN does not require either identification of the parameters of interest or the nuisance parameters.
• However, for orthogonal moments to be informative, the efficient Fisher Information matrix for the parameter must be non-zero (though possibly singular).