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Estimating multivariate density and its derivatives for mixed measurement error data. (English) Zbl 1520.62010

Summary: 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, including 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.

MSC:

62G07 Density estimation
62H12 Estimation in multivariate analysis
62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference

Software:

KernSmooth
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Full Text: DOI

References:

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