I have been reading about isotonic regression and it seems like a great method that will give one a monotone regression function estimator and, moreover, is free of any tuning parameters.
Why are people still using alternative approaches to such estimation (e.g. constrained splines, etc.) that require a choice of a tuning parameter?
Isotonic regression
By Alexeicolin - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=23732999
As seen in the image, and suggested (partly) by the name, isotonic regression is monotonic increasing or monotonic decreasing. Thus, it would not be appropriate for fitting distributions that have left and right tails. Also, unlike B-splines, it does not fit derivatives, so it will not approximate smooth curves like most distribution functions. It may be useful to approximate heuristically the predicted values, but would not be especially useful for extrapolation beyond the extreme values of the x-axis data.
