...$X$1
For the methods discussed here, we generally need the linearity condition, the $\mbox{E}(A'x\vert B'x)$ is a linear function for $B'x$, where $A$ is any matrix, and $B$ is a matrix such that $F(y\vert x) = F(y\vert B'x)$. This condition holds, for example, if the marginal distribution of $X$ is normal, although that assumption is much stronger than is needed. See Cook (1998), Cook and Weisberg (1994, 1999) for more discussion.
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