Abstract
A binary classification problem is considered, where the posteriori probability is estimated by the nonparametric kernel regression estimate with naive kernel. The excess error probability of the corresponding plug-in decision classification rule according to the error probability of the Bayes decision is studied such that the excess error probability is decomposed into approximation and estimation error. A general formula is derived for the approximation error. Under a weak margin condition and various smoothness conditions, tight upper bounds are presented on the approximation error. By a Berry-Esseen type central limit theorem a general expression for the estimation error is shown.
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This work was supported in part by the National Development Agency (NFÜ, Hungary) as part of the project Introduction of Cognitive Methods for UAV Collision Avoidance Using Millimeter Wave Radar, (grant no.: KMR-12-1-2012-0008).
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Döring, M., Györfi, L., Walk, H. (2016). Exact Rate of Convergence of Kernel-Based Classification Rule. In: Matwin, S., Mielniczuk, J. (eds) Challenges in Computational Statistics and Data Mining. Studies in Computational Intelligence, vol 605. Springer, Cham. https://doi.org/10.1007/978-3-319-18781-5_5
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DOI: https://doi.org/10.1007/978-3-319-18781-5_5
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