Abstract
Many people are aware of some substantial recent controversy in smoothing. The current discussion is partly a consequence of this. I have observed a number of differing ideas as to “what the debate is all about”. Of these various ideas, I view the main ones as being:
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I1.
Should one use local polynomial (degree higher than 0) or local constant (i.e. conventional kernel methods) smoothers?
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I2.
Should one choose “smoothing windows” using the same width everywhere, or a width based on nearest neighbor considerations?
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I3.
Is LO(W)ESS the best possible way to do smoothing?
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I4.
Is mathematical analysis a useful tool in statistics?
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I5.
Are there effective methods of choosing the bandwidth from the data? Are these good enough to become defaults in software packages?
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References
Akaike, H. (1954) An approximation to the density function, Annals of the Institute of Statistical Mathematics, 6, 127–132.
Cook, R. D. and Weisberg, S. (1994) Regression Graphics, Wiley, New York.
Fix, E. and Hodges, J. L. (1951) Discriminatory analysis - nonparametric discrimination: consistency properties. Report No. 4, Project No. 21–29-004, USAF School of Aviation Medicine, Randolph Field, Texas.
Fix, E. and Hodges, J. L. (1989) Discriminatory analysis - nonparametric discrimination: consistency properties, International Statistical Review, 57, 238–247.
Fan, J. and Marron, J. S. (1994) Fast implementations of nonparametric curve estimators, Journal of Computational and Graphical Statistics, 3,35–56.
Hall, P. and Marron, J. S. (1995) On the role of the ridge parameter in local linear smoothing, unpublished manuscript.
Lejeune, M. (1984) Optimization in nonparametric regression, Compstat 1984 (Proceedings in Computational Statistics), eds. T. Havranek, Z. Sidak, and M. Novak, Physica Verlag, Vienna, 421–426.
Lejeune, M. (1984) Estimation non-paramétrique par noyaux: régression polynomiale mobile, Revue de Statistiques Appliquées, 33, 43–67.
Marron, J. S. (1995a) Presentation of smoothers: the family approach, unpublished manuscript.
Marron, J. S. (1995b) Visual understanding of higher order kernels, to appear in Journal of Computational and Graphical Statistics.
Marron, J. S. and Nolan, D. (1989) Canonical kernels for density estimation, Statistics and Probability Letters, 7, 195–199.
Marron, J. S. and Udina, F. (1995) Interactive local bandwidth choice, unpublished manuscript.
Marron, J. S. and Wand, M. P. (1992) Exact mean integrated squared error, Annals of Statistics, 20, 712–736.
Minnotte, M.C. and Scott, D. W. (1993). The Mode Tree: A Tool for Visualization of Nonparametric Density Features, Computational and Graphical Statistics, 2, 51–68.
Silverman, B. W. (1981) Using kernel estimates to investigate modality, Journal of the Royal Statistical Society, Series B, 43, 97–99.
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© 1996 Physica-Verlag Heidelberg
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Marron, J.S. (1996). Rejoinder. In: Härdle, W., Schimek, M.G. (eds) Statistical Theory and Computational Aspects of Smoothing. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-48425-4_8
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DOI: https://doi.org/10.1007/978-3-642-48425-4_8
Publisher Name: Physica-Verlag HD
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