Let $m_{y|x}(y|x)=e^x$ denote the conditional median of $Y$ given $X$. What is the approach to derive unconditional median of $Y$---- $m_y(y)$? Any relationship between the conditional and unconditional medians?
Any suggestion will be appreciated.
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The unconditional median will be between the smallest possible conditional median and the largest possible conditional median – Henry Feb 11 '18 at 00:34
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Thanks. Is there any reference to read? When is it possible for the median of conditional median=unconditional median, like mean and conditional mean? – Vincent Feb 11 '18 at 00:53