Summary
The paper considers the problem of nonparametric regression with emphasis on controlling the number of local extremes and on resistance against patches of outliers. The robust taut string method is introduced and robustness properties are discussed. An automatic procedure is described.
* Research supported in part by Sonderforschungsbereich 478, University of Dortmund
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References
I. Barrodale and F.D.K. Roberts. An improved algorithm for discrete 11 linear approximation. SIAM J. Numer. Anal., 10:839–848, 1973.
P. Chaudhuri and J.S. Marron. Sizer for exploration of structures in curves. J. Am. Statist. Assoc., 94:807–823, 1999.
L. Davies and U. Gather. The identification of multiple outliers (with discussion). J. Am. Statist. Assoc., 88:782–801, 1993.
P.L. Davies. Data features. Statistica Neerlandica, 49:183–245, 1995.
P.L. Davies and A. Kovac. Densities, spectral densities and modality. Submitted, 2001a.
P.L. Davies and A. Kovac. Local extremes, runs, strings and multiresolution (with discussion). Ann. Statist., 29:1–65,2001b.
D.L. Donoho, I.M. Johnstone, G. Kerkyacharian, and D. Picard. Wavelet shrinkage: Asymptopia? J. Royal Statist. Soc. B, 57:371–394,1995.
L. Dümbgen. Confidence bands for convex median curves using sign-tests. Preprint A-01–05, 2001.
L. Dümbgen and R. Johns. Confidence bands for isotonic median curves using sign-tests. Preprint A-00–24, 2000.
J. Fan and I. Gijbels. Local polynomial modelling and its applications. Chapman and Hall, London, 1996.
E. Mammen and S. van de Geer. Locally adaptive regression splines. Ann. Statist., 25:387–413,1997.
E.A. Nadaraya. On estimating regression. Theory of Probability and its Applications, 10: 186–190,1964.
B.W. Silverman. Some aspects of the spline smoothing approach to non-parametric regression curve fitting. J. Royal Statist. Soc. B,47:1–52,1985.
G.S. Watson. Smooth regression analysis. Sankhya, Series A, 26:101–116, 1964.
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© 2003 Springer-Verlag Berlin Heidelberg
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Kovac, A. (2003). Robust Nonparametric Regression and Modality. In: Dutter, R., Filzmoser, P., Gather, U., Rousseeuw, P.J. (eds) Developments in Robust Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57338-5_18
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DOI: https://doi.org/10.1007/978-3-642-57338-5_18
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-642-63241-9
Online ISBN: 978-3-642-57338-5
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