About Message 18.
If you want us to estimate the distribution of the median in Pb 2, do you then just want us to this for a few different sample sizes. (You said a range of sample sizes, which seem to mean that you would like to see the behavior over different sizes, but if we have to estimate the actual distribution for each sample size, it'll be hard to report as a function over a range...)
An alternative would be to estimate the confidence intervals obtained for the median, and report this over a range of sample sizes. Would this be fine?

About Pb 1,
what do you mean by "error bars" for giving a forecast of the MSE of our final model ?

/m25 reply: I think Hyun Min Kang is right that the Wilcoxon rank-sum test is not a test for whether or not two medians are the same in general. It is a test of H0: two distributions have the same shape and the same median versus H1: the two distributions have the same shape but different medians.

/m26 answer: For 2(a) we are interested in the variance of the bootstrap-based estimate of the median, compared to the variance of (for example) the sample mean. Each of these variances is a function of the sample size N, so the efficiency is a function of N.

For 1, I mean give a forecast confidence interval of the MSE of your model, so you can evaluate if the true MSE falls within this confidence interval.

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