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Nonparametric methods for inference in the presence of instrumental variables. (English) Zbl 1084.62033
Summary: We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the “difficulty” of which depends on eigenvalues of a certain integral operator which is determined by the joint density of endogenous and instrumental variables. We delineate the role played by problem difficulty in determining both the optimal convergence rate and the appropriate choice of smoothing parameter.

MSC:
62G08 Nonparametric regression and quantile regression
62H12 Estimation in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
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