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Bandwidth Selection for Kernel Estimates

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Combinatorial Methods in Density Estimation

Part of the book series: Springer Series in Statistics ((SSS))

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Abstract

This chapter is about the choice of the bandwidth (or smoothing factor) h ∈ (0, ∞) of the standard kernel estimate

$$ {f_{n,h}}(x) = \frac{1}{{n{h^d}}}\sum\limits_{i = 1}^n {K\left( {\frac{{x - {X_i}}}{h}} \right)} . $$

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§11.8. References

  • L. Devroye, “Universal smoothing factor selection in density estimation: Theory and practice (with discussion),” Test, vol. 6, pp. 223–320, 1997.

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  • L. Devroye, L. Györfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New York, 1996.

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  • L. Devroye and G. Lugosi, “A universally acceptable smoothing factor for kernel density estimation,” Annals of Statistics, vol. 24, pp. 2499–2512, 1996.

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  • L. Devroye and G. Lugosi, “Non-asymptotic universal smoothing factors, kernel complexity and Yatracos classes,” Annals of Statistics, vol. 25, pp. 2626–2637, 1997.

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  • L. Devroye and C. S. Penrod, “Distribution-free lower bounds in density estimation,” Annals of Statistics, vol. 12, pp. 1250–1262, 1984.

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© 2001 Springer Science+Business Media New York

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Devroye, L., Lugosi, G. (2001). Bandwidth Selection for Kernel Estimates. In: Combinatorial Methods in Density Estimation. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0125-7_11

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  • DOI: https://doi.org/10.1007/978-1-4613-0125-7_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6527-6

  • Online ISBN: 978-1-4613-0125-7

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