As far as I know, one can calculate the relative standard error from the standard deviation of a data sample. I am looking for the Median Absolute Deviation equivalent for standard error.
Does one exist? Also which methods exist to calculate the relative standard error, that do not require the standard deviation?
Best Answer
When you say standard error, you should be talking about the standard error of something, such as the standard error of the sample mean.
Similarly you could for example talk about the median absolute deviation of the sample median. It is possible to calculate this, at least as an approximation for large samples.
It is well known that for a continuous random variable with population median $m$, continuous probability density of the median $f(m)$ and a large odd sample size $n$, the sample median is approximately normally distributed with median $m$ and variance $\frac{1}{4 n f(m)^2}$, i.e. with median absolute deviation approximately $\dfrac{\Phi^{-1}\left(\frac34 \right)}{2 \sqrt{n} f(m)}$ where $\frac{\Phi^{-1}\left(\frac34 \right)}{2} \approx 0.337$.
If you want to have this as a relative median absolute deviation of the sample median, then presumably you divide by $m$.