On Deconvolution as a First Stage Nonparametric Estimator

We reconsider Taupin's (2001) Integrated Nonlinear Regression (INLR) estimator for a nonlinear regression with a mismeasured covariate. We find that if we restrict the distribution of the measurement error to a class of distributions with restricted support, then much weaker smoothness assumptions than hers suffice to ensure [image omitted] consistency of the estimator. In addition, we show that the INLR estimator remains consistent under these weaker smoothness assumptions if the support of the measurement error distribution expands with the sample size. In that case the estimator remains also asymptotically normal with a rate of convergence that is arbitrarily close to [image omitted]. Our results show that deconvolution can be used in a nonparametric first step without imposing restrictive smoothness assumptions on the parametric model.