In this article, we propose a class of partial deconvolution kernel estimators for the nonparametric regression function when some covariates are measured with error and some are not. The estimation procedure combines the classical kernel methodology and the deconvolution kernel technique. According to whether the measurement error is ordinarily smooth or supersmooth, we establish the optimal local and global convergence rates for these proposed estimators, and the optimal bandwidths are also identified. Furthermore, lower bounds for the convergence rates of all possible estimators for the nonparametric regression functions are developed. It is shown that, in both the super and ordinarily smooth cases, the convergence rates of the proposed partial deconvolution kernel estimators attain the lower bound. The Canadian Journal of Statistics 48: 535–560; 2020 © 2020 Statistical Society of Canada

中文翻译：

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非参数回归中的部分反卷积估计

在本文中，当一些协变量被测量为误差而另一些则没有时，我们为非参数回归函数提出了一类部分反卷积核估计。估计过程结合了经典核方法和反卷积核技术。根据测量误差通常是平滑的还是超平滑的，我们为这些拟议的估算器建立了最佳的局部和全局收敛速度，并确定了最佳带宽。此外，针对非参数回归函数的所有可能估计量的收敛速度的下界也得到了发展。结果表明，在超光滑情况和通常光滑情况下，所提出的部分反卷积核估计量的收敛速度均达到下限。《加拿大统计杂志》 48：535–560；2020©2020加拿大统计学会