×

zbMATH — the first resource for mathematics

Sliced inverse median difference regression. (English) Zbl 1458.62139
Summary: In this paper we propose a sufficient dimension reduction algorithm based on the difference of inverse medians. The classic methodology based on inverse means in each slice was recently extended, by using inverse medians, to robustify existing methodology at the presence of outliers. Our effort is focused on using differences between inverse medians in pairs of slices. We demonstrate that our method outperforms existing methods at the presence of outliers. We also propose a second algorithm which is not affected by the ordering of slices when the response variable is categorical with no underlying ordering of its values.
MSC:
62G08 Nonparametric regression and quantile regression
62H12 Estimation in multivariate analysis
62G35 Nonparametric robustness
Software:
robustbase; UCI-ml
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Artemiou, A.; Tian, L., Using slice inverse mean difference for sufficient dimension reduction, Stat Probab Lett, 106, 184-190 (2015) · Zbl 1398.62085
[2] Brown, BM, Statistical uses of the spatial mean, J R Stat Soc B, 45, 25-30 (1983) · Zbl 0508.62046
[3] Bura, E.; Yang, J., Dimension estimation in sufficient dimension reduction: a unifying approach, J Multivar Anal, 102, 130-142 (2011) · Zbl 1206.62107
[4] Christou, E., Robust dimension reduction using sliced inverse median regression, Stat Pap (2018) · Zbl 1452.62248
[5] Cook, RD, Regression graphics: ideas for studying regressions through graphics (1998), New York: Wiley, New York · Zbl 0903.62001
[6] Cook, RD; Weisberg, S., Discussion of “sliced inverse regression for dimension reduction”, J Am Stat Assoc, 86, 316-342 (1991)
[7] Dong, Y.; Yu, Z.; Zhu, L., Robust inverse regression for dimension reduction, J Multivar Anal, 134, 71-81 (2015) · Zbl 1305.62207
[8] Dua D, Karra-Taniskidou E (2017) UCI machine learning repository. http://archive.ics.uci.edu/ml. University of California, School of Information and Computer Science, Irvine, CA
[9] Gather U, Hilker T, Becker C (2001) A robustified version of sliced inverse regression. In: Fernholz LT, Morgenthaler S, Stahel W (eds) Statistics in genetics and in the environmental sciences. Birkhäuser: Basel, pp 147-157
[10] Hamidieh, K., A data-driven statistical model for predicting the critical temperature of a superconductor, Comput Mater Sci, 154, 346-354 (2018)
[11] Hettmansperger, TP; McKean, JW, Robust nonparametric statistical methods (1998), London, New York: Arnold/Wiley, London, New York
[12] Li, B., Sufficient dimension reduction. Methods and applications with R (2018), New York: Chapman and Hall/CRC, New York
[13] Li, B.; Artemiou, A.; Li, L., Principal support vector machine for linear and nonlinear sufficient dimension reduction, Ann Stat, 39, 3182-3210 (2011) · Zbl 1246.62153
[14] Li, B.; Wang, S., On directional regression for dimension reduction, J Am Stat Assoc, 102, 997-1008 (2007) · Zbl 05564427
[15] Li, K-C, Sliced inverse regression for dimension reduction (with discussion), J Am Stat Assoc, 86, 316-342 (1991)
[16] Luo, W.; Li, B., Combining eigenvalues and variation of eigenvectors for order determination, Biometrika, 103, 875-887 (2016) · Zbl 07072160
[17] Maechler M, Rousseeuw P, Croux C, Todorov V, Ruckstuhl A, Salibian-Barrera M, Verbeke T, Koller M, Conceicao ELT, di Palma MA (2018) Robustbase: Basic Robust Statistics R package version 0.93-3. http://CRAN.R-project.org/package=robustbase
[18] Shao, Y.; Cook, RD; Weisberg, S., Marginal tests with sliced average variance estimation, Biometrika, 94, 285-296 (2007) · Zbl 1133.62032
[19] Yeh, I-C, Modeling of strength of high performance concrete using artificial neural networks, Cem Concr Res, 28, 12, 1797-1808 (1998)
[20] Yin, X.; Li, B.; Cook, RD, Successive direction extraction for estimating the central subspace in a multiple-index regression, J Multivar Anal, 99, 1733-1757 (2008) · Zbl 1144.62030
[21] Zhu, LP; Zhu, LX; Feng, ZH, Dimension reduction in regression through cumulative slicing estimation, J Am Stat Assoc, 105, 1455-1466 (2010) · Zbl 1388.62121
[22] Zhu, LX; Miao, B.; Peng, H., On sliced inverse regression with large dimensional covariates, J Am Stat Assoc, 101, 630-643 (2006) · Zbl 1119.62331
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.