JSM 2005 Online Program

Abstract #302911

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Activity Number:	486
Type:	Contributed
Date/Time:	Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
Sponsor:	Section on Nonparametric Statistics
Abstract - #302911
Title:	Large Sample Properties of Shape Restricted Regression Estimators with Smoothness Adjustments
Author(s):	Jayanta Pal*+
Companies:	University of Michigan
Address:	1929 Plymouth Road, Ann Arbor, MI, 48105, United States
Keywords:	Smoothing spline ; Monotonic functions ; Green's function ; Asymptotic normality ; Kernel regression ; Greatest convex minorant
Abstract:	The problem under consideration is the isotonic regression with a smoothness penalty. The shape-restricted smooth estimator was characterized as a solution to a set of recurrence relations in Tantiyaswasdikul and Woodroofe (J.S.P.I. 1994). Using a closely related Green's function, the estimator can be approximately represented as a kernel regression estimator. Under regularity conditions of the underlying regression function, asymptotic normality of the estimator is established. The crux of the argument relates the difference equation and their continuous analog, showing the proximity of their respective solutions. The method is extended to monotone parameter exponential family problems. It is compared to the usual Pool-Adjacent-Violator estimator in either case in simulations. It exhibits a better performance in the central area of the covariates and gradually worsens toward the endpoints. However, it relieves the spiking problem. Also, asymptotic normality implies that the final confidence interval can be worked out without too much computation.

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