I have a set of values $x_i\quad i=1,…,N$ of which I can calculate the median M. Each $x_i$ has an error $\delta x_i$. The $x_i$ values are the result of a maximum likelyhood estimation and their error is calculated using the Cramer-Rao inequality.

How could I proceed to calculate the error on the median $\delta M$?

Some time ago I asked a similar question but at the time I did not consider the error on the $x_i$ values. How this additional uncertainty modifies the answer/way of thinking?

  • $\begingroup$ Could you be more specific about what an "error" is? Unless those errors can be translated into something like a joint distribution, or at a minimum can be given finite bounds, then obtaining an objective answer looks hopeless. $\endgroup$ – whuber Mar 1 '16 at 17:07

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