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DATA SPHERING: SOME PROPERTIES AND APPLICATIONS

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JIAN ZHANG

*Institute of Systems Science, Academia Sinica, Beijing 100080, China*
(Received September 30, 1996; revised May 15, 1997)

**Abstract.**
Centring-then-sphering is a very
important pretreatment in data analysis. The purpose of
this paper is to study the asymptotic behavior of the
sphering matrix based on the square root decomposition
(SRD for short) and its applications. A sufficient
condition is given under which SRD has nondegenerate
asymptotic distribution. As examples, some commonly used
and affine equivariant estimates of the dispersion matrix
are shown to satisfy this condition. The case when the
population dispersion matrix varies is also treated.
Applications to projection pursuit (PP) are presented. It
is shown that for elliptically symmetric distributions
the PP index after centring-then-sphering is independent
of the underlying population location and dispersion.

*Key words and phrases*:
Sphering, dispersion
matrix, invariance, asymptotics, projection pursuit.

**Source**
( TeX ,
DVI ,
PS )