2,019 research outputs found
Asymptotics for sliced average variance estimation
In this paper, we systematically study the consistency of sliced average
variance estimation (SAVE). The findings reveal that when the response is
continuous, the asymptotic behavior of SAVE is rather different from that of
sliced inverse regression (SIR). SIR can achieve consistency even
when each slice contains only two data points. However, SAVE cannot be
consistent and it even turns out to be not consistent when each
slice contains a fixed number of data points that do not depend on n, where n
is the sample size. These results theoretically confirm the notion that SAVE is
more sensitive to the number of slices than SIR. Taking this into account, a
bias correction is recommended in order to allow SAVE to be
consistent. In contrast, when the response is discrete and takes finite values,
consistency can be achieved. Therefore, an approximation through
discretization, which is commonly used in practice, is studied. A simulation
study is carried out for the purposes of illustration.Comment: Published at http://dx.doi.org/10.1214/009053606000001091 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Estimating sufficient reductions of the predictors in abundant high-dimensional regressions
We study the asymptotic behavior of a class of methods for sufficient
dimension reduction in high-dimension regressions, as the sample size and
number of predictors grow in various alignments. It is demonstrated that these
methods are consistent in a variety of settings, particularly in abundant
regressions where most predictors contribute some information on the response,
and oracle rates are possible. Simulation results are presented to support the
theoretical conclusion.Comment: Published in at http://dx.doi.org/10.1214/11-AOS962 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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