Open Access
VOL. 54 | 2007 Shape restricted regression with random Bernstein polynomials
I-Shou Chang, Li-Chu Chien, Chao A. Hsiung, Chi-Chung Wen, Yuh-Jenn Wu

Editor(s) Regina Liu, William Strawderman, Cun-Hui Zhang

IMS Lecture Notes Monogr. Ser., 2007: 187-202 (2007) DOI: 10.1214/074921707000000157


Shape restricted regressions, including isotonic regression and concave regression as special cases, are studied using priors on Bernstein polynomials and Markov chain Monte Carlo methods. These priors have large supports, select only smooth functions, can easily incorporate geometric information into the prior, and can be generated without computational difficulty. Algorithms generating priors and posteriors are proposed, and simulation studies are conducted to illustrate the performance of this approach. Comparisons with the density-regression method of Dette et al. (2006) are included.


Published: 1 January 2007
First available in Project Euclid: 4 December 2007

MathSciNet: MR2459189

Digital Object Identifier: 10.1214/074921707000000157

Primary: 62F15 , 62G08
Secondary: 65D10

Keywords: Bayesian concave regression , Bayesian isotonic regression , geometric prior , Markov chain Monte Carlo , Metropolis-Hastings reversible jump algorithm

Rights: Copyright © 2007, Institute of Mathematical Statistics

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