2009/02/12 by Christoph Breunig, Breunig, Christoph, Jan Johannes +1
Engineering · Mathematics · #Control Systems and Identification #FOS: Mathematics #Numerical methods in inverse problems #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.0902.2103
openalex publication_date 2009/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed estimator is based on dimension reduction and additional thresholding. The minimax optimal rate of convergence of the estimator is derived assuming that the structural function and the representer of the linear functional belong to some ellipsoids which are in a certain sense linked to the conditional expectation operator of Z given W. We illustrate these results by considering classical smoothness assumptions.