Semi-parametric Estimation in a Single-index Model with Endogenous Variables

Birke, Melanie;Van Bellegem, Sébastien;Van Keilegom, Ingrid
(2017) Scandinavian Journal of Statistics : theory and applications — Vol. 44, n° 1, p. 168-191 (2017)

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Abstract
We consider a semiparametric single-index model and suppose that endogeneity is present in the explanatory variables. The presence of an instrument is assumed, that is, noncorrelated with the error term.We propose an estimator of the parametric component of the model, which is the solution of an ill-posed inverse problem. The estimator is shown to be asymptotically normal under certain regularity conditions. A simulation study is conducted to illustrate the finite sample performance of the proposed estimator.
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Birke, M., Van Bellegem, S., & Van Keilegom, I. (2017). Semi-parametric Estimation in a Single-index Model with Endogenous Variables. Scandinavian Journal of Statistics : theory and applications, 44(1), 168-191. https://doi.org/10.1111/sjos.12247 (Original work published 2017)