care of the fact that the basis functions $\vv^\alpha$ used in  are smoothed with a gaussian window of $R_s=10\hmpc$ in width. The expression (\[eq:sigv\]) is obtained assuming the linear relation $H_0 f \delta =-{\bf \nabla} \cdot \vv(\vx)$ between the density contrast, $\delta$, and $\vv(\vx)$ [@Peeb80].

The MLE and reconstructed bulks are similar especially at large distances $r>40\hmpc$. This is because, the data covers space more isotropically at larger distances. Figure (\[fig:scatt15\]) clearly demonstrates that  will not cause a significant artificial under-estimation of large bulk flows such as reported in [@feldwh10]. To further, ascertain that our   derived bulk flow is robust, the blue circles in figure (\[fig:btotn\]) the amplitude of the  bulk flow reconstructed using basis functions generated from a $\Lambda$CDM7 power spectrum but with a scalar index $n=0.75$ and $\sigma_8=1$. The results are very similar to the  bulk flow shown in figure (\[fig:btot\]) despite the significantly enhanced large scale power. The agreement is particularly striking at large distances.

Comparison with cosmological models {#sec:comp}
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Figure (\[fig:btot\]) indicates that the estimated bulk flows are consistent with the theoretical expectations. But the errors are strongly correlated and a proper statistical analysis must take into account the covariance of the errors. Our large 