Estimating multivariate density and its derivatives for mixed measurement error data

In this paper, we propose a nonparametric mixed kernel estimator for a multivariate density function and its derivatives when the data are contaminated with different sources of measurement errors. The proposed estimator is a mixture of the classical and the deconvolution kernels, accounting for the error-free and error-prone variables, respectively. Large sample properties of the proposed nonparametric estimator, includ-ing the order of the mean squares error, the consistency, and the asymptotic normality, are thoroughly investigated. The optimal convergence rates among all nonparametric estimators for different measurement error structures are derived, and it is shown that the proposed mixed kernel estimators achieve the optimal convergence rate. A simulation study is conducted to evaluate the finite sample performance of the proposed estimators. (C) 2022 Elsevier Inc. All rights reserved.