A Bayesian approach to nonparametric monotone function estimation

Shively, Thomas S. and Sager, Thomas W. and Walker, Stephen G. (2009) A Bayesian approach to nonparametric monotone function estimation. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71 (1). pp. 159-175. ISSN 1369-7412. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate. The small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods. Asymptotic results are also given that show that Bayesian methods provide consistent function estimators for a large class of smooth functions. An example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple-regression model where two functions are constrained to be monotone.

Item Type: Article
Uncontrolled keywords: Asymptotic properties; Markov chain Monte Carlo sampling scheme; Mixture prior distributions; Regression splines; Small sample properties
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Judith Broom
Date Deposited: 17 Mar 2009 12:58
Last Modified: 29 Apr 2014 15:44
Resource URI: https://kar.kent.ac.uk/id/eprint/12679 (The current URI for this page, for reference purposes)
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