Penalized Isotonic Regression

• Activity Number: 188
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jiwen Wu*+ and Mary Meyer and Jean Opsomer
• Companies: Colorado State University and Colorado State University and Colorado State University
• Keywords: Isotonic regression ; Penalized estimation ; Multivariate model ; Consistent estimator

Abstract

With a long history, a lot methods have been developed to calculate the solutions of isotonic regression problems. It is known that the estimators are inconsistency at boundaries for univariate and multivariate models, and it is called "spiking" problem. A penalty on the range of the variables is proposed to correct the spiking problem on the edges. A new algorithm (Meyer 2013) for multiple isotonic regression based on cone projection is applied; it is computationally efficient for large sample sizes and good for inference making. The theoretical properties of the penalized estimator are discussed and extended to model with two covariates, and simulation show the improvements at edges.