Abstract: The isotonic regression problem with a smoothness penalty is considered. The shape-restricted smooth estimator was characterized as a solution to a set of recurrence relations by Tantiyaswasdikul and Woodroofe (1994). Using a related Green's function, the estimator can be represented as a kernel regression estimator. Under regularity conditions on the underlying regression function, asymptotic normality of the estimator is established for a large range of choices of the tuning parameter.
Key words and phrases: Asymptotic normality, Green's function, monotonic function, smoothing spline.