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Bootstrap CIs can be systematically too short because CIs are meant to capture the uncertainty in the data regarding the parameter estimator, but the bootstrap CI only accounts for the variation visible …

Many bootstrap replications are drawn in order to approximate (in a standard situation) the distribution of i.i.d. samples from the empirical distribution. … Note by the way that i.i.d. sampling from the empirical distribution will produce uniform probabilities over ordered rather than distinct samples, meaning that if you want to emulate the true bootstrap …

If the sample size is very small, bootstrap can't generate that much variation, so it won't work that well, but then hardly anything nonparametric will work better. … As always there is no fixed rule about sample sizes... bootstrap is worse with a smaller sample, but all alternative approaches are worse, too, so it is not clear cut. …

This addresses question 2 only, I don't know the answer to 1. You generated data from a proper Gaussian distribution. A Gaussian distribution has a very, very low probability to generate outliers, bec …

In general you need to know in advance what your null hypothesis of interest is, and then the bootstrap test null hypothesis needs to be chosen so that it is in line with this, as explained in the book … the mean of the underlying distribution, and say your $t(X)=5$ (observed mean on your data), then $\hat F_0$ would be the empirical distribution of your observations minus 5 (or if you run a parametric bootstrap …

that bootstrap works well in the same situations in which non-bootstrap statistics may also work well with large samples (see Enno Mammen, When does bootstrap work? … Otherwise how the characteristics of a certain bootstrap test relate to the characteristics of a classical (non-bootstrap) test that is supposed to test the same null hypothesis surely depends on the exact …

Formally, the null hypothesis of the test is that the two means are equal, because the distribution of the test statistic is simulated by bootstrap assuming that the means are equal. … This is however not different from the standard (non-bootstrap) two-sample t-test. …

In the explained situation you cannot use the bootstrap to say anything about the variability of the median of the individual countries, because this variability is governed by the variability of observations … Any bootstrap you can do will be informative only about the variability of the statistic your bootstrap over all countries, so if you bootstrap the median, it will tell you about the variability of the …

This is not normally assumed in (nonparametric) bootstrap and the interval is constructed from bootstrap statistics quantiles (there is more than one way of doing this, see Wikipedia on bootstrap confidence … bootstrap" doesn't do that, see the Wikipedia page). …

So indeed one doesn't need the bootstrap for this. The bootstrap can be used to estimate the variance of a statistic for which a straight general method as for the mean does not exist. … Furthermore, the bootstrap can be used to assess the shape of the sampling distribution, which even for the mean is unknown unless the underlying distribution is known. …

Bootstrap tests on the other hand are usually biased. … So in general it's wrong to say that bootstrap is always preferable for CIs and permutation tests are always better for tests, however where a permutation test can be done it is usually better than a bootstrap …

Which, if you so wish, is the assumption of bootstrap. (e) Bootstrap can be very unstable if the dataset is small; it can also be unstable if there are not enough bootstrap replicates. … In any case use a generous number of bootstrap samples if you want bootstrap. (3) In case the dataset is reasonably big and doesn't show the specific robustness issues for which the robust estimator is …