Nonparametric function estimation subject to monotonicity, convexity and other shape constraints

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 funct...

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Bibliographic Details
Published in:Journal of econometrics 2011-04, Vol.161 (2), p.166-181
Main Authors: Shively, Thomas S., Walker, Stephen G., Damien, Paul
Format: Article
Language:English
Subjects:
Algorithms
Applications
Bayesian analysis
Bayesian method
Econometrics
Estimating techniques
Estimation
Exact sciences and technology
Fixed-knot splines
Fixed-knot splines Free-knot splines Log-concave likelihood functions MCMC sampling algorithm Small sample properties
Free-knot splines
Insurance, economics, finance
Log-concave likelihood functions
Mathematics
MCMC sampling algorithm
Model testing
Monte Carlo simulation
Nonparametric inference
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Parametric inference
Probability and statistics
Regression analysis
Sampling
Sciences and techniques of general use
Significance tests
Small sample properties
Statistical models
Statistics
Studies
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Summary: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.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2010.12.001