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• W4366758995 abstract "AbstractWe propose two novel bandwidth selection procedures for the nonparametric regression model with classical measurement error in the regressors. Each method evaluates the prediction errors of the regression using a second (density) deconvolution. The first approach uses a typical leave-one-out cross-validation criterion, while the second applies a bootstrap approach and the concept of out-of-bag prediction. We show the asymptotic validity of both procedures and compare them to the SIMEX method in a Monte Carlo study. As well as dramatically reducing computational cost, the methods proposed in this article lead to lower mean integrated squared error (MISE) compared to the current state-of-the-art.Keywords: Measurement error modelsdeconvolutionnonparametric regressionbandwidth selectionJEL Classification: C14 AcknowledgmentsThe authors acknowledge financial supports from the SMU Dedman College Research Fund (12-412268) (Dong) and the Aarhus University Research Fund (AUFF-26852) (Taylor).Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 Delaigle et al. (Citation2015) and Kato and Sasaki (Citation2019) also provide methods (closely related to Delaigle and Hall, Citation2008) for bandwidth selection in this model; however, these methods are designed to ensure the validity of confidence bands rather than optimizing the estimation of m.2 Note that we only consider global bandwidth selection; the choice of a local bandwidth which changes over the range of the regressor is beyond the scope of this paper. For local bandwidth choice, one may extend the conventional approach to minimize an estimate of the (approximate) MSE E[{m̂(x;h)−m(x)}2] for a given x. It would also be interesting to see if recent developments in coverage-error optimal bandwidths (Calonico et al., Citation2018, Citation2020) could be extended to the nonparametric deconvolution context.3 It is interesting to note that our deconvolution approach to estimate R(h) in Equation(4)(4) R(h)=E[∬{y−m̂(x;h)}2fYX(y,x)dydx],(4) may be applied to other estimation methods to construct m̂(x;h), where the meaning of the tuning parameter h changes. For example, Davezies and Barbanchon (Citation2017) and Bartalotti et al. (Citation2020) proposed nonparametric regression estimators in the context of regression discontinuity designs, where auxiliary data are available. Although they allow nonclassical measurement errors, it would be interesting to see if our approach could be adapted to suggest bandwidth selectors for their estimators under the classical measurement error setting.4 For the error-free case, Wong (Citation1983) considered the average squared error loss n−1∑j=1n{m̂(Xj;h)−m(Xj)}2 as the criterion to select the bandwidth. Since X is unobservable in our contaminated case, it is natural to consider the integrated squared error loss Rn(h).5 Results for the known measurement error case and the unknown case with X from a Laplace distribution were qualitatively similar.Additional informationFundingThis work was financially supported by the SMU Dedman College Research Fund (12-412268) (Dong) and the Aarhus University Research Fund (AUFF-26852) (Taylor)." @default.
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• W4366758995 date "2023-04-21" @default.
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• W4366758995 title "Bandwidth selection for nonparametric regression with errors-in-variables" @default.
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