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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.
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