Local Isotonic Regression

• Activity Number: 268
• Type: Topic Contributed
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Derick R. Peterson*+
• Companies: University of Rochester
• Keywords: local monotonic regression ; nonparametric regression ; local polynomial regression

Abstract

A new Local Isotonic (LOIS) regression estimator is proposed for the standard nonparametric regression problem. The idea is to approximate the regression function at each point by a local isotonic regression rather than, say, a local polynomial one. Since this local model is clearly more flexible than that of local linear regression, itself a locally monotone model, the LOIS regression estimator has smaller bias at most points. Moreover, in stark contrast to local polynomial regression, LOIS regression is very insensitive to the choice of bandwidth unless the regression function oscillates frequently. And if the data are monotone then, for any bandwidth, LOIS reproduces the data, is thus conditionally unbiased at each observation, and is equivalent to the nonparametric maximum likelihood estimator for monotone regression functions. Since the price to be paid for the added flexibility of the local model is increased variability, and asymptotically this price is a steep one, the performance of LOIS for practical sample sizes is investigated via a simulation study.