×

zbMATH — the first resource for mathematics

Partial central subspace and sliced average variance estimation. (English) Zbl 1156.62032
Summary: Sliced average variance estimation is one of many methods for estimating the central subspace. It was shown to be more comprehensive than sliced inverse regression in the sense that it consistently estimates the central subspace under mild conditions while sliced inverse regression may estimate only a proper subset of the central subspace. We extend this method to regressions with qualitative predictors. We also provide tests of dimension and a marginal coordinate hypothesis test. We apply the method to a data set concerning lakes infested by Eurasian Watermilfoil, and compare this new method to the partial inverse regression estimator.

MSC:
62G08 Nonparametric regression and quantile regression
62J99 Linear inference, regression
62P12 Applications of statistics to environmental and related topics
62E20 Asymptotic distribution theory in statistics
62H12 Estimation in multivariate analysis
Software:
ARC
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chiaromonte, F.; Cook, R.D.; Li, B., Sufficient dimension reduction in regressions with categorical predictors, Ann. statist., 30, 475-497, (2002) · Zbl 1012.62036
[2] Cook, R.D., On the interpretation of regression plots, J. amer. statist. assoc., 89, 177-189, (1994) · Zbl 0791.62066
[3] Cook, R.D., Testing predictor contributions in sufficient dimension reduction, Ann. statist., 32, 1062-1092, (2004) · Zbl 1092.62046
[4] Cook, R.D.; Lee, H., Dimension reduction in regressions with a binary response, J. amer. statist. assoc., 94, 1187-1200, (1999) · Zbl 1072.62619
[5] Cook, R.D.; Ni, L., Sufficient dimension reduction via inverse regression: a minimum discrepancy approach, J. amer. statist. assoc., 100, 410-428, (2005) · Zbl 1117.62312
[6] Cook, R.D.; Weisberg, S., Discussion on ‘sliced inverse regression for dimension reduction’, J. amer. statist. assoc., 86, 328-332, (1991) · Zbl 1353.62037
[7] Cook, R.D.; Weisberg, S., Applied regression including computing and graphics, (1999), Wiley New York · Zbl 0928.62045
[8] Li, B.; Wang, S., On directional regression for dimension reduction, J. amer. statist. assoc., 102, 997-1008, (2007) · Zbl 05564427
[9] Li, K.-C., Sliced inverse regression for dimension reduction (with discussion), J. amer. statist. assoc., 86, 316-342, (1991)
[10] Ni, L.; Cook, R.D., Sufficient dimension reduction in regressions across heterogeneous subpopulations, J. roy. statist. soc. ser. B, 68, 89-107, (2006) · Zbl 1141.62042
[11] Schupp, D., 1992. An ecological classification of Minnesota lakes with associated fish communities. Minnesota Department of Natural Resources, Investigational Report 417.
[12] Shao, Y.; Cook, R.D.; Weisberg, S., Marginal tests with sliced average variance estimation, Biometrika, 94, 285-296, (2007) · Zbl 1133.62032
[13] Smith, C.S.; Barko, J.W., Ecology of Eurasian watermilfoil, J. aquatic plant management, 28, 55-64, (1990)
[14] Tyler, D., Asymptotic inference for eigenvectors, Ann. statist., 9, 725-736, (1981) · Zbl 0474.62051
[15] Wen, X.; Cook, R.D., Optimal sufficient dimension reduction in regressions with categorical predictors, J. statist. plann. inference, 137, 1961-1978, (2007) · Zbl 1118.62043
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.