Statistica Sinica 15(2005), 1069-1079
ASYMPTOTIC DISTRIBUTIONS FOR DIMENSION
REDUCTION IN THE SIR-II METHOD
Xiangrong Yin and Lynne Seymour
The University of Georgia
Abstract:
The asymptotic distribution of the test statistic for testing the dimensionality
in the SIR-II method
is derived and shown to be a linear combination of 
random
variables under weak assumptions. This statistic is based on Li's (1991)
sequential test statistic
for sliced inverse regression (SIR). Also presented is a simulation study of
the result.
Key words and phrases:
Asymptotic distributions, Central subspaces,
Dimension-reduction subspaces, Regression graphics.