Smoothed Nonparametric Derivative Estimation using Weighted Difference Quotients

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. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

Authors

• Yu Liu
• Kris De Brabanter

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