Likelihood ratio tests for monotonic functions with regions of flatness

Music City Center 

A typical assumption in the asymptotic analysis of estimators of monotonic functions is that they are strictly monotonic, eliminating the possibility for regions of flatness. We characterize the asymptotic behavior of the monotonic regression estimator for a function f at a fixed point x when f is constant in some neighborhood of x. Further, we extend the results on likelihood ratio testing from Banerjee and Wellner (2001) and Groeneboom and Jongbloed (2015) to these regions of flatness.

Monotonic Regression

Nonparametric Regression

Shape constraints

Asymptotics

Likelihood ratio testing 

Section on Nonparametric Statistics