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

Title:
Nonparametric function estimation subject to monotonicity, convexity and other shape constraints
Authors:
SHIVELY, Thomas S, WALKER, Stephen G, DAMIEN, Paul
Source:
Journal of econometrics. 161(2):166-181
Publisher Information:
Amsterdam: Elsevier, 2011.
Publication Year:
2011
Physical Description:
print, 3/4 p
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Probabilités et statistiques, Probability and statistics, Statistiques, Statistics, Inférence paramétrique, Parametric inference, Inférence non paramétrique, Nonparametric inference, Applications, Assurances, économie, finance, Insurance, economics, finance, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Approximation numérique, Numerical approximation, Algorithme, Algorithm, Algoritmo, Analyse numérique, Numerical analysis, Análisis numérico, Approximation numérique, Numerical approximation, Aproximación numérica, Approximation spline, Spline approximation, Aproximación esplín, Chaîne Markov, Markov chain, Cadena Markov, Convexité, Convexity, Convexidad, Echantillonnage, Sampling, Muestreo, Econométrie, Econometrics, Econometría, Estimation Bayes, Bayes estimation, Estimación Bayes, Estimation non paramétrique, Non parametric estimation, Estimación no paramétrica, Estimation statistique, Statistical estimation, Estimación estadística, Fonction concave, Concave function, Función cóncava, Fonction forme, Shape function, Función forma, Fonction régulière, Smooth function, Función regular, Fonction vraisemblance, Likelihood function, Función verosimilitud, Méthode Gauss, Gauss method, Método Gauss, Méthode Monte Carlo, Monte Carlo method, Método Monte Carlo, Méthode non paramétrique, Non parametric method, Método no paramétrico, Méthode semiparamétrique, Semiparametric method, Método semiparamétrico, Méthode statistique, Statistical method, Método estadístico, Simulation, Simulación, Théorie contrainte, Constraint theory, 41A15, 62F30, 62G05, 65D07, Analyse bayésienne, Estimation fonction, Function estimation, Estimation paramétrique, Estimation sous contrainte, Constrained estimation, Log vraisemblance, Log likelihood, Spline régression, Regression spline, C11-Bayesian analysis, C14-Semiparametric and nonparametric, Fixed-knot splines, Free-knot splines, Log-concave likelihood functions, MCMC sampling algorithm, Small sample properties, methods
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
University of Texas at Austin, United States
University of Kent, United Kingdom
ISSN:
0304-4076
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=23943483
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.23943483
Database:
PASCAL Archive

Further Information

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.