1) Is there a generally unbiased estimator for the quantiles of a distribution?
If not - I would be glad for an explanation (proof?) of why not.
2) Also (if not), is there a specific family of distributions for which there is an unbiased estimator for their quantiles?
3) And lastly, is the median a special case for the general rule? (for example, is there a general unbiased estimator for the median?)