practice we write the corrected estimate of the bulk flow $\vB_{_{\rm  corr}}(r)$ from the raw bulk $ \vB_{_{ \rm raw}}(r)$ (directly reconstructed by either  or MLE) as $\vB_{_{\rm corr}}(r)=C_1 \vB_{_{ \rm raw}}(r) +C_2$ where $C_1$ is the ratio of the rms values of the true to raw bulk flows and $C_2$ is a constant term which accounts for the offset between the true and raw bulk flows.

In all panels of figure (\[fig:scatt\]), the mock $\vace$ are tightly scattered around their corresponding regression lines. The scatter in $\vmle$ appears to be more significant. To quantify the scatter between the reconstructed and true bulk flows, we plot, in figure (\[fig:costh\]), the cumulative fraction, $P<(\theta)$, of mock catalogues for which the angle between estimated and true bulk flows is less than $\theta$. The solid blue and red dashed curves refer to  and MLE, respectively, while thick and thin to bulk flows within $40\hmpc$ and $100\hmpc$, also respectively. The curves are computed after employing the correction to the systematic bias as explained above. The performance of  is excellent. For $40\hmpc$, the direction of $\vace$ is recovered within $3^\circ$ for about $68\%$ of the mocks. For $100\hmpc$ this uncertainty increased to $7^\circ$. The  method 