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Smoothed nonparametric derivative estimation using weighted difference quotients. (English) Zbl 07255096
Summary: Derivatives play an important role in bandwidth selection methods (e.g., plug-ins), data analysis and bias-corrected confidence intervals. Therefore, obtaining accurate derivative information is crucial. Although many derivative estimation methods exist, the majority require a fixed design assumption. In this paper, we propose an effective and fully data-driven framework to estimate the first and second order derivative in random design. We establish the asymptotic properties of the proposed derivative estimator, and also propose a fast selection method for the tuning parameters. The performance and flexibility of the method is illustrated via an extensive simulation study.
MSC:
68T05 Learning and adaptive systems in artificial intelligence
Software:
locpol; pspline; kedd; ks
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