Journal
JOURNAL OF ECONOMETRICS
Volume 161, Issue 2, Pages 166-181Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jeconom.2010.12.001
Keywords
Fixed-knot splines; Free-knot splines; Log-concave likelihood functions; MCMC sampling algorithm; Small sample properties
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Funding
- McCombs School of Business at the University of Texas at Austin
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This paper uses free-knot and fixed-knot regression splines in a Bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log-concave likelihood functions. The shape constraints we consider include monotonicity, convexity and functions with a single minimum. A computationally efficient MCMC sampling algorithm is developed that converges faster than previous methods for non-Gaussian models. Simulation results indicate the monotonically constrained function estimates have good small sample properties relative to (i) unconstrained function estimates, and (ii) function estimates obtained from other constrained estimation methods when such methods exist. Also, asymptotic results show the methodology provides consistent estimates for a large class of smooth functions. Two detailed illustrations exemplify the ideas. (C) 2010 Elsevier B.V. All rights reserved.
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