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.
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