Let's assume that we have two samples $\{X_i\}_{i=1..N}$ and $\{Y_i\}_{i=1..M}$ corresponding to random variables $X$ and $Y$. Let there also be a sample $\{Z_i\}_{i=1..K}$ corresponding to random variable $Z$. Assume that $Z$ is unknown mixture of $X$ and $Y$, i.e. $f_Z = \alpha f_X + (1-\alpha) f_Y$.
Is there any way to estimate the alpha coefficient without resorting to parametric hypotheses about $X$ and $Y$? Since we have their samples, it seems possible with the help of kernel density estimation.
P.S. Articles about the nonparametric EM method that I found immediately go into the wilds. But the current case seems to be simple.