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Sliced average variance estimation

Sliced average variance estimation, or save, was proposed by Cook and Weisberg (1991). As with sir, we slice the range of $Y$ into $h$ slices, but rather than compute the within-slice mean we compute within-slice covariance matrices. If $C_i$ is the weighted within slice sample covariance matrix in slice $i$, then the matrix $\hat{M}$ is given by

\begin{displaymath}
\hat{M} = \frac{1}{n}\sum g_i(I-C_i)^2
\end{displaymath}

where $g_i$ is the sum of the weights in the slice; if all weights are equal, then the $g_i$ 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