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Using SIMEX for smoothing-parameter choice in errors-in-variables problems

by Aurore Delaigle and Peter Hall

SIMEX methods are attractive for solving curve estimation problems in errors-in-variables regression, using parametric or semiparametric techniques. However, nonparametric approaches are generally of quite a different type, being based on, for example, kernels, local-linear modelling, ridging, orthogonal series, or splines. All of these techniques involve the challenging (and not well studied) issue of empirical smoothing parameter choice.We show that SIMEX can be used effectively for selecting smoothing parameters when applying nonparametric methods to errors-in-variable regression. In particular, we suggest an approach based on multiple error-inflated (or remeasured) data sets and extrapolation.

KEYWORDS: Bandwidth; Bootstrap; Cross-validation; Ill-posed problem; Inverse problem; Kernel estimation; Monte Carlo simulation; Nonparametric curve estimation; Nonparametric regression; Parametric model; Statistical smoothing.

Full text of the paper (pdf), which has just appeared in the Journal of the American Statistical Association.