Nonparametric estimation of additive models with errors-in-variables

Hao Dong, Taisuke Otsu and Luke Taylor

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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.

Keywords: backfitting; classical measurement error; nonparametric additive regression; ridge regularization; series estimation (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2022-11-28
New Economics Papers: this item is included in nep-dcm
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Published in Econometric Reviews, 28, November, 2022, 41(10), pp. 1164 - 1204. ISSN: 0747-4938

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http://eprints.lse.ac.uk/116007/ Open access version. (application/pdf)

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Journal Article: Nonparametric estimation of additive models with errors-in-variables (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:116007

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