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Universal smoothing factor selection in density estimation: theory and practice |
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| Authors: | Duc Devroye J. Beirlant R. Cao R. Fraiman P. Hall M. C. Jones Gábor Lugosi E. Mammen J. S. Marron C. Sánchez-Sellero J. de Uña F. Udina L. Devroye |
| Affiliation: | 1. School of Computer Science, McGill University, H3A 2K6, Montreal, Canada 2. Katholieke Universiteit Leuven, Belgium 3. Universidad de la Coru?a, Spain 4. Universidad de la República, Uruguay 5. The Australian National University, Australia 6. The Open University, UK 7. Universitat Pompeu Fabra, Spain 8. Universit?t Heidelberg, Germany 9. University of North Carolina, USA 10. Universidad de Santiago de Compostela, Spain 11. Universidad de Vigo, Spain 12. Universitat Pompeu Fabra, Spain |
| Abstract: | In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, forall densities in all dimensions, theL 1 error of the corresponding kernel estimate is not larger than 3+∈ times the error of the estimate with the optimal smoothing factor plus a constant times $sqrt {log n/n}$ , wheren is the sample size, and the constant only depends on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for eachn. The estimate uses ideas from the minimum distance estimation work of Yatracos. We present a practical implementation of this estimate, report on some comparative results, and highlight some key properties of the new method. |
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