Nonparametric estimation of additive models with errors-in-variables

In the estimation of nonparametric additive models, conventional methods, such as backfitting and series approximation, cannot be applied when measurement error is present in a covariate. This paper proposes a two-stage estimator for such models. In the first stage, to adapt to the additive structur...

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Bibliographic Details
Published inEconometric reviews Vol. 41; no. 10; pp. 1164 - 1204
Main Authors Dong, Hao, Otsu, Taisuke, Taylor, Luke
Format Journal Article
LanguageEnglish
Published New York Taylor & Francis 2022
Taylor & Francis Ltd
Subjects
Additives
Approximation
Backfitting
classical measurement error
Convergence
Econometrics
Error analysis
Measurement
nonparametric additive regression
Nonparametric statistics
Normality
ridge regularization
series estimation
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Summary:In the estimation of nonparametric additive models, conventional methods, such as backfitting and series approximation, cannot be applied when measurement error is present in a covariate. This paper proposes a two-stage estimator for such models. In the first stage, to adapt to the additive structure, we use a series approximation together with a ridge approach to deal with the ill-posedness brought by mismeasurement. We derive the uniform convergence rate of this first-stage estimator and characterize how the measurement error slows down the convergence rate for ordinary/super smooth cases. To establish the limiting distribution, we construct a second-stage estimator via one-step backfitting with a deconvolution kernel using the first-stage estimator. The asymptotic normality of the second-stage estimator is established for ordinary/super smooth measurement error cases. Finally, a Monte Carlo study and an empirical application highlight the applicability of the estimator.
ISSN:0747-4938
1532-4168
DOI:10.1080/07474938.2022.2127076