# Approaches for extracting single-year age estimates from age-buckets

I'm trying to estimate a binary function of $Y$~$Bernouli(p_{i})$ where $p_{i}=f(age)$ where f is an unknown continuous function. There are obviously a lot of methods to try to reconstruct f (splines, Gaussian processes, etc), but what if my age observations are collapsed into buckets (18-29, 30-44,etc)?

Obviously, it's impossible to reconstruct f even with infinite data. And reconstruction of f is going to depend fairly strongly on assumptions about the nature of f. But this seems like it should be a common problem and I'm curious what approaches people have used/would use.

edit 7/14/2014:I should clarify that in this case, I have a pretty good distribution of the overall distribution of age in the population.