AN ADAPTIVE COMPOSITE QUANTILE APPROACH TO DIMENSION REDUCTION
Kong, Efang
(2014)
AN ADAPTIVE COMPOSITE QUANTILE APPROACH TO DIMENSION REDUCTION.
Annals of Statistics,
42
(4).
pp. 1657-1688.
ISSN 0090-5364.
Abstract
Su?cient dimension reduction [Li (1991)] has long been a promi-
nent issue in multivariate nonparametric regression analysis. To un-
cover the central dimension reduction space, we propose in this pa-
per an adaptive composite quantile approach. Compared to existing
methods, (1) it requires minimal assumptions and is capable of reveal-
ing all dimension reduction directions; (2) it is robust against outliers;
and (3) it is structure-adaptive, thus more e?cient. Asymptotic re-
sults are proved and numerical examples are provided, including a
real data analysis.
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