is significantly superior to MLE. The thin blue and thick dashed lines almost overlap, meaning that the performance of   for $100\hmpc$ is as as good as that of MLE for $40\hmpc$. For $r=100\hmpc$, MLE recovers the direction only within $27^\circ$ for $68\% $ of the mocks.

Figure (\[fig:db\]) plots the differential probability distribution function, $P(\delta B)$, where $\delta B$ refers to the difference in all cartesian components between estimated and true bulk flows, from the 2200 mocks. The notation of the lines is the same as in the previous figure and as displayed in the figure. The figure also indicates $\sigma$, the rms value of $\delta B$ for the plotted cases. The low values of $\sigma$ corresponding to  demonstrate its excellent ability at recovering the true bulk. The performance of MLE is good, but less satisfactory.

Results {#sec:res}
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The results of the application of the  and MLE methods to recover the bulk flow from the real SFI++ TF catalogue are summarized in figures (\[fig:unb\])–(\[fig:btot\]). The bulk flows are reconstructed for spheres centered on the Milky-Way and of radii from $r=20\hmpc$ to $100\hmpc$ in steps of $10\hmpc$. The smallest radius is chosen large enough so that nonlinear effects are not 