Shape restricted regression with random Bernstein polynomials
Abstract
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.
Cite
@article{arxiv.0708.1054,
title = {Shape restricted regression with random Bernstein polynomials},
author = {I-Shou Chang and Li-Chu Chien and Chao A. Hsiung and Chi-Chung Wen and Yuh-Jenn Wu},
journal= {arXiv preprint arXiv:0708.1054},
year = {2009}
}
Comments
Published at http://dx.doi.org/10.1214/074921707000000157 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)