Say you had a sample of ages from a population, but the ages are in buckets...Such as <1, 1-4, 5-14, 15-24, ..., 55-64, 65+...And you want to get an estimate for the average of the age distribution and get a confidence interval for the mean.
I know if you assume a parametric distribution you could just estimate by maximum likelihood, using likelihoods over the given interval. Simple. But what if you have no idea what age distribution to use? Is there some kind of non-parametric approach that could be used?