Abstract: We study the asymptotic properties of a Tikhonov regularised (TiR) estimator of a func- tional parameter based on a minimum distance principle for nonparametric conditional moment restrictions. The estimator is computationally tractable and even takes a closed form in the linear case. We derive its asymptotic Mean Integrated Squared Error (MISE), its rate of convergence and its pointwise asymptotic normality under a regularisation para- meter depending on the sample size. The optimal value of the regularisation parameter is characterised. We illustrate our theoretical findings and the small sample properties with simulation results for two numerical examples. We also discuss two data driven selection procedures of the regularisation parameter via a spectral representation and a subsampling approximation of the MISE. Finally, we provide an empirical application to nonparametric estimation of an Engel curve.
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