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Sufficient dimension reduction in regressions with categorical predictors. (English) Zbl 1012.62036
Summary: We describe how the theory of sufficient dimension reduction, and a well-known inference method for it (sliced inverse regression), can be extended to regression analyses involving both quantitative and categorical predictor variables. As statistics faces an increasing need for effective analysis strategies for high-dimensional data, the results we present significantly widen the applicative scope of sufficient dimension reduction and open the way for a new class of theoretical and methodological developments.

MSC:
62G08 Nonparametric regression and quantile regression
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62G09 Nonparametric statistical resampling methods
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[17] UNIVERSITY PARK, PENNSYLVANIA 16802 E-MAIL: chiaro@stat.psu.edu R. D. COOK SCHOOL OF STATISTICS 1994 BUFORD AVENUE UNIVERSITY OF MINNESOTA ST. PAUL, MINNESOTA 55108 E-MAIL: dennis@stat.umn.edu B. LI DEPARTMENT OF STATISTICS PENNSYLVANIA STATE UNIVERSITY 326 THOMAS BUILDING UNIVERSITY PARK, PENNSYLVANIA 16802 E-MAIL: bing@stat.psu.edu
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