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Sliced average variance estimation, or save, was proposed by Cook and
Weisberg (1991).  As with sir, we slice the range of  into
 into  slices,
but rather than compute the within-slice mean we compute within-slice
covariance matrices.  If
 slices,
but rather than compute the within-slice mean we compute within-slice
covariance matrices.  If  is the weighted within slice sample covariance
matrix in slice
 is the weighted within slice sample covariance
matrix in slice  ,
then the matrix
,
then the matrix  is given by
 is given by
where  is the sum of the weights in the slice; if all weights are
equal, then the
 is the sum of the weights in the slice; if all weights are
equal, then the  are just the number of observations in each slice.
save looks at
second moment information and may miss first-moment information,
particularly it may miss linear trends.
Output for save is similar to sir, except that no asymptotic tests have
been developed.  However, tests of dimension based on a permutation test are
available; see Section 4.
 are just the number of observations in each slice.
save looks at
second moment information and may miss first-moment information,
particularly it may miss linear trends.
Output for save is similar to sir, except that no asymptotic tests have
been developed.  However, tests of dimension based on a permutation test are
available; see Section 4.
Sandy Weisberg
2002-01-10