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Approximation Error

Since $ \vert I_{m,n+q} \vert < L^{-q} \vert I_{m,n} \vert$ for $F >
L$, the relative error in $I_{m,n+q}$ is bounded by

\begin{displaymath}
\vert \epsilon_q \vert < (-1)^q(\frac{D_2}{D_1})^q\left(\pro...
...q}\frac{(2n-D_1)}{(2n+D_2)}\right)\frac{2(1+q)-D_1}{2} L^{-q}.
\end{displaymath} (49)

This is also the relative error in $\log(p)$ since it is proportional to $I_{m,n}$. In practice, unlike the T score approximation the error improves with increased iterations and is well within the required error with 20 iterations for $F > 1$ and for any degrees of freedom.



Mark Jenkinson 2004-01-21