I would like to sample from a bivariate conditional distribution $F(y_1, y_2 |X_1 = x_1, ..., X_p=x_p)$, where the distribution is determined non-parametrically. How can I sample from such a distribution?
1 Answer
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Once one observes the realisation $$X_1 = x_1, ..., X_o=x_o$$ the values $x_1,\ldots,x_o$ are fixed and known. Hence the conditional cdf (I assume this is a cdf) $$F(y_1, y_2 |X_1 = x_1, ..., X_o=x_o)$$ is a function of $(y_1,y_2)$ only and a regular cdf, for which standard simulation techniques apply.
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$\begingroup$ Thank you! But if the cdf $F$ is an empirical distribution (non-differentiable), this standard simulation technique does not work in my opinion. That's what I am struggeling with. $\endgroup$– anjo1659Commented Jul 1, 2022 at 9:47
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$\begingroup$ @anjo1659: The question does not mention anything like this so you should rephrase it to reflect on your actual difficulties and repost it as another question. $\endgroup$– Xi'anCommented Jul 1, 2022 at 11:21