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 Vol. 161; no. 2; pp. 166 - 181
Main Authors: Shively, Thomas S., Walker, Stephen G., Damien, Paul
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.04.2011
Elsevier
Elsevier Sequoia S.A
Series:Journal of Econometrics
Subjects:
Algorithms
Applications
Bayesian analysis
Bayesian method
Constraints
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
Function
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
Property
Regression analysis
Sampling
Sciences and techniques of general use
Significance tests
Simulation
Small sample properties
Statistical models
Statistics
Studies
MCMC sampling algorithm
C11—Bayesian analysis
Small sample properties
Fixed-knot splines
Log-concave likelihood functions
C14—Semiparametric and nonparametric methods
Free-knot splines
Shape function
methods
Non parametric method
Non parametric estimation
Spline approximation
Numerical approximation
Markov chain
C14-Semiparametric and nonparametric
C11-Bayesian analysis
Smooth function
Log likelihood
Constraint theory
Regression spline
Convexity
Sampling
Likelihood function
Bayes estimation
Monte Carlo method
Gauss method
Statistical estimation
Constrained estimation
Semiparametric method
Algorithm
Concave function
Statistical method
Function estimation
Numerical analysis
Simulation
Econometrics
ISSN:0304-4076, 1872-6895
Online Access:Get full text
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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.
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ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2010.12.001