Abstract
In curve estimation, running M-estimates are a natural generalization of Kernel-type smoothers (moving averages). We find the rate of convergence that can be expected from these estimates and the leading bias and variance terms. We also explain the effect of twicing for Kernel-type smoothers and give some rationale for its use in robust curve estimation.
Keywords
- Asymptotic Behavior
- Variance Term
- Curve Estimation
- Bias Term
- Optimal Kernel
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References
Tukey, J. W., EDA Exploratory Data Analysis. Addison-Wesley (1977).
Velleman, P. Robust nonlinear data smoothers: Definitions and recommendations. Natl. Acad. Sci. USA (1977), Vol. 74, No. 2, pp. 434–436.
Mallows, C. Some theory of non-linear smoothers. To appear in Ann. Statist. (July 1980).
Huber, P. J. Robust Smoothing. To appear in Proc. of the ARO Workshop on Robust Statistics (April 1978). Academic Press (in press).
Huber, P. J., Robust estimation of a location parameter. Ann. Math. Statist. (1964), Vol. 35, No. 1, pp. 73–101.
Epanechnikov, V. A., Nonparametric estimates of a multivariate probability density. Theor. Prob. Appl. (1969), Vol. 14, pp. 153–158.
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© 1979 Springer-Verlag
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Stuetzle, W., Mittal, Y. (1979). Some comments on the asymptotic behavior of robust smoothers. In: Gasser, T., Rosenblatt, M. (eds) Smoothing Techniques for Curve Estimation. Lecture Notes in Mathematics, vol 757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098497
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DOI: https://doi.org/10.1007/BFb0098497
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09706-8
Online ISBN: 978-3-540-38475-5
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