LARGE SAMPLE PROPERTIES OF SHAPE RESTRICTED REGRESSION ESTIMATORS WITH SMOOTHNESS ADJUSTMENTS

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 estima- tor. 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.