Rate-optimal nonparametric estimation in classical and Berkson errors-in-variables problems |
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Authors: | Aurore Delaigle Alexander Meister |
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Institution: | a Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia b Institut für Mathematik, Universität Rostock, D-18051 Rostock, Germany |
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Abstract: | We consider nonparametric estimation of a regression curve when the data are observed with Berkson errors or with a mixture of classical and Berkson errors. In this context, other existing nonparametric procedures can either estimate the regression curve consistently on a very small interval or require complicated inversion of an estimator of the Fourier transform of a nonparametric regression estimator. We introduce a new estimation procedure which is simpler to implement, and study its asymptotic properties. We derive convergence rates which are faster than those previously obtained in the literature, and we prove that these rates are optimal. We suggest a data-driven bandwidth selector and apply our method to some simulated examples. |
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Keywords: | Bandwidth Deconvolution Kernel methods Local polynomial Measurement error Minimax convergence rates Nonparametric regression |
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