Hall, Peter; Horowitz, Joel L.
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...[Show more]
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