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Title: Semiparametric estimation with isotonic estimator plugged-in Authors:  Mengshan Xu - London School of Economics and Political Science (United Kingdom) [presenting]
Abstract: A semiparametric estimator is studied, where the moment condition associated with it contains a nuisance monotone function, which is estimated nonparametrically by isotonic regression. We show that the properties of isotonic regression satisfy the framework of Newey (1994), and we obtain a semiparametric estimator which is root-n consistent and asymptotically normally distributed. Furthermore, we show that in the case that the monotone nuisance function is a conditional mean, the associated score/moment function with an isotonic estimator plugged in will automatically satisfy Neyman orthogonality, and semiparametric efficiency can be achieved in many cases. This structure can help practitioners to obtain tuning-parameter-free estimators for many semiparametric models, including partial linear model, single-index model and particularly, average treatment effect model.