Nonparametric estimation of additive models with errors-in-variables

Hao Dong, Taisuke Otsu and Luke Taylor

Econometric Reviews, 2022, vol. 41, issue 10, 1164-1204

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.

Date: 2022
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DOI: 10.1080/07474938.2022.2127076

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