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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Vydané v:	Journal of econometrics Ročník 161; číslo 2; s. 166 - 181
Hlavní autori:	Shively, Thomas S., Walker, Stephen G., Damien, Paul
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.04.2011 Elsevier Elsevier Sequoia S.A
Edícia:	Journal of Econometrics
Predmet:	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
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Popis
Shrnutí:	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.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2
ISSN:	0304-4076 1872-6895
DOI:	10.1016/j.jeconom.2010.12.001