Nonparametric estimation of additive models with errors-in-variables
针对协变量存在测量误差时非参数加性模型无法用传统方法估计的问题，提出两阶段估计法，推导了收敛速度与渐近正态性，并通过模拟和实证验证了方法的有效性。
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.