Abstract In this paper, a nonparametric estimator for the regression function is constructed when the covariates are contaminated with the multivariate Laplace measurement error. The proposed estimator is based upon a simple relationship between the regression function and the conditional expectation of the regression function given the proxy data, as well as the second derivative of this expectation. Large sample properties of the proposed estimator, including the consistency and asymptotic normality, are established. The theoretical optimal bandwidth based on asymptotic integrated mean squared error is derived, and a data-driven bandwidth selector is recommended. Finite sample performance of the proposed estimator is evaluated by a simulation study.

中文翻译：

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具有伯克森拉普拉斯测量误差的非参数回归估计

摘要 在本文中，当协变量受到多元拉普拉斯测量误差的污染时，构造了回归函数的非参数估计量。建议的估计量基于回归函数与给定代理数据的回归函数的条件期望之间的简单关系，以及该期望的二阶导数。建立了建议估计量的大样本特性，包括一致性和渐近正态性。推导出基于渐近积分均方误差的理论最优带宽，并推荐使用数据驱动的带宽选择器。所提议的估计器的有限样本性能通过模拟研究进行评估。