We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate b. Such a genealogical tree is usually called a...

The fact that signal-in-noise filtering model can serve as a prototype for nonparametric regression is well known and it is widely used in the nonparametric curve estimation theory. So far the only known examples showing that the equivalence may not hold have been about homoscedastic regressions...