Non-technical conditions for validity of nonparametric bootstrap confidence intervals I am rather ignorant about nonparametric bootstrap. Assume the same context as in this question:  ${(x_i)}_{i=1}^m$ and ${(y_i)}_{i=1}^n$ are independent data samples, the $x_i$ are independent replicates from a distribution with expectation $\mu_X$ and similarly the $y_i$ are independent replicates from a distribution with expectation $\mu_Y$. We estimate the ratio $\theta=\mu_X/\mu_Y$ by the ratio $\hat\theta = \bar x / \bar y$ of the two sample means. Under which conditions the quantiles of the boostrap samples of $\hat\theta$ provide a valid confidence interval about $\theta$ ?
I am not interested in the finest required technical conditions (such as a $L^{1+\epsilon}$-integrability condition), but rather in more easy conditions which are reasonable to assume for common real datasets.
EDIT: I am not interested in trivial counter-examples too. For instance I assume the the $y_i$ cannot be negative (the support of their distribution is an interval of strictly positive numbers) and the unknown distributions are discrete or continuous distributions.
EDIT: Maybe what I expect to understand is more clear if I ask a different question : assuming the previous 'edit' and strong distributional assumptions (such as $L^2$), under which conditions have we a valid bootstrap confidence interval about $f(\mu_X,\mu_Y)$ for a suitable function $f$ when using the bootstrap samples of the estimate $f(\bar x, \bar y)$ ? Is the unbiasedness of this estimate a required condition ?
 A: In their book, An Introduction to the Bootstrap (Chapman and Hall, New York 1994),  Efron and Tibshirani give an example of estimating a ratio with the patch data study. The ratio of the averages is a biased estimate for the average of the ratio.  So Efron and Tibshirani use the patch data to show how the bootstrap can correct for this bias.
These data are based on a clinical trial where the effect of a hormonal patch produced at a new manufacturing plant is compared to the effect at the old (approved) manufacturing plant.  The parameter of interest in this problem is 
$$\theta = \frac{E(\text{new})-E(\text{placebo})}{E(\text{old})-E(\text{placebo})}.$$ 
$E(.)$ is the expected level of hormone in the bloodstream by "new" = patch produced at new plant, "old" = patch produced at the approved plant, and "placebo" = patch without hormone.
The FDA requirement for approval of the new manufacturing plant is that the new patch produces at least 80% of the effect that the old patch produced over placebo.  So the idea is to estimate $\theta$ and show via a confidence interval (or hypothesis testing) that it is greater than 0.80; or, equivalently, that $1-\theta$ is less than 0.20.
In this problem the numerator and denominator both have distributions concentrated on the positive half of the real line and bounded away from 0.  So the problem that Bill Huber mentioned does not occur.  In the book, Efron and Tibshirani compute the biased point estimate along with its bootstrap estimate of bias.  They show that the bias-corrected estimate of $1-\theta$ is well below 0.20.  Bootstrap confidence intervals could be used for this by again separately bootstrapping the two samples and computing the ratio estimates, say $B$ times, by Monte Carlo.
