 transmission power spectrum ( $n > 2$ is required for convergence). It is for this reason that a direct comparison cannot be made between the above simple estimates and a test-case shown by Croft et al. [-@croft98] in which the initial power spectrum has $n =
1$. In fact, for a scale-free initial power spectrum of $k^{-n}$, the stable-clustering mass power spectrum at high $k$ should be $k^{-6/(5-n)}$ (). For $n=1$, this means the high $k$ mass power spectrum asymptotes to $k^{-1.5}$, which is still not enough to regularize the integral for the transmission power spectrum (eq. \[\[inverse\]\] together with eq. \[\[Wlinear\]\]). It is likely that in their test-case, an effective ultraviolet cut-off is imposed by the finite resolution of the simulation, or else the true nonlinear redshift-distortion kernel provides an effective regularization. Note, however, that there is no small-scale Jeans smoothing to help here because Croft et al. [-@croft98] used N-body-only simulations.

Nonetheless, we should emphasize that while, on large scales, the direction of the systematic error of method I is on firm ground (i.e. systematic flattening), the size of the error, on the other hand, is subject to further investigation. We have used linear theory in §\[perturb\] to estimate the magnitude of this effect. The linear calculation gives us the effective “bias-factor” (let us call it $b_{\beta}$, which equals $2-0.7 (\gamma-1)$ in eq. \[\[Wlinear\]\]) associated with the distortion parameter $\beta_f$ (i.e. $\beta_f = f_\Omega /
b_{\beta}$), but this might not be the correct $b_{\beta}$ in the presence of nonlinear fluctuations on small scales.

For instance, according to arguments by Scherrer & Weinberg (), the galaxy-bias $b_g$ (different from $b_{\beta}$ above, see below), defined as the ratio of the galaxy to mass two-point function on large scales (where galaxy is related to mass by a local transformation), generally involves all the higher derivatives of the local transformation around $\delta = 0$ i.e. not just the 