The biweight midvariance $\zeta^2$ is a measure of scale that is more robust to non-normal distributions. It is defined as follows by [1] in three steps. For observations $X_i$, $i = 1,2,\cdots,n$, with median $M$:
$$\begin{aligned} Y_i &= \frac{X_i - M}{9\times MAD}\\ \\ a_i &= \begin{cases}1, & \text{if } |Y_i| < 1\\ 0, & \text{if } |Y_i| \geq 1\end{cases}\\ \\ \zeta &= \frac{\sqrt{n}\sqrt{\sum a_i (X_i - M)^2 (1 - Y_i^2)^4}}{|\sum a_i(1-Y_i^2)(1-5Y_i^2)|}\\ \end{aligned}$$
Where $MAD$ is the median absolute deviation of $X$. The biweight midvariance is then defined to be $\zeta^2$.
The question I have is regarding the definition of $Y_i$. In two implementation in R (bivar function in WRS package[2] and r.bw function in asbio package[3]), the denominator of $Y_i$ is multiplied by the 0.75 standard normal quantile $z_{0.75}$:
$$Y_i = \frac{X_i - M}{9\times z_{0.75} \times MAD}$$
Could someone please explain to me for what reason(s) one would multiply the median absolute deviation by $z_{0.75}$?
Many thanks!
[1] Wilcox, Rand R. Introduction to robust estimation and hypothesis testing. Academic Press, 2012.
[2] WRS http://www.nicebread.de/software/WRS/index.html
[3] asbio http://www.inside-r.org/packages/cran/asbio/docs/R.bw