Somewhat misleading argument involving O_p

[mb706]

Chapter 6 seems to make the argument that the sample median's error is larger / converges slower because its $O_p$ expression has a larger constant factor than for the sample mean:

10EconometricTheorems/07-op.Rmd

Line 218 in 4a65b92

Now we can see that the big-op of the sample median's estimating error is "slower" (read: larger) than the big-op of the sample mean, meaning that the sample mean converges on the true parameter with fewer observations than the sample median.

However, $O_p$ is indifferent to constant factors, and $O_p(\sqrt{\frac{\pi}{2}}\cdot n^{-1/2}) = O_p(n^{-1/2})$. It might be clearer to state this fact here: both the sample mean and sample median have error $O_p(n^{-1/2})$, but the limiting variance of the sample mean is lower by a factor of $\pi/2$.