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On a Robust MaxEnt Process Regression Model with Sample-Selection

In a regression analysis, a sample-selection bias arises when a dependent variable is partially observed as a result of the sample selection. This study introduces a Maximum Entropy (MaxEnt) process regression model that assumes a MaxEnt prior distribution for its nonparametric regression function a...

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Autores principales: Kim, Hea-Jung, Bae, Mihyang, Jin, Daehwa
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512777/
https://www.ncbi.nlm.nih.gov/pubmed/33265353
http://dx.doi.org/10.3390/e20040262
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author Kim, Hea-Jung
Bae, Mihyang
Jin, Daehwa
author_facet Kim, Hea-Jung
Bae, Mihyang
Jin, Daehwa
author_sort Kim, Hea-Jung
collection PubMed
description In a regression analysis, a sample-selection bias arises when a dependent variable is partially observed as a result of the sample selection. This study introduces a Maximum Entropy (MaxEnt) process regression model that assumes a MaxEnt prior distribution for its nonparametric regression function and finds that the MaxEnt process regression model includes the well-known Gaussian process regression (GPR) model as a special case. Then, this special MaxEnt process regression model, i.e., the GPR model, is generalized to obtain a robust sample-selection Gaussian process regression (RSGPR) model that deals with non-normal data in the sample selection. Various properties of the RSGPR model are established, including the stochastic representation, distributional hierarchy, and magnitude of the sample-selection bias. These properties are used in the paper to develop a hierarchical Bayesian methodology to estimate the model. This involves a simple and computationally feasible Markov chain Monte Carlo algorithm that avoids analytical or numerical derivatives of the log-likelihood function of the model. The performance of the RSGPR model in terms of the sample-selection bias correction, robustness to non-normality, and prediction, is demonstrated through results in simulations that attest to its good finite-sample performance.
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spelling pubmed-75127772020-11-09 On a Robust MaxEnt Process Regression Model with Sample-Selection Kim, Hea-Jung Bae, Mihyang Jin, Daehwa Entropy (Basel) Article In a regression analysis, a sample-selection bias arises when a dependent variable is partially observed as a result of the sample selection. This study introduces a Maximum Entropy (MaxEnt) process regression model that assumes a MaxEnt prior distribution for its nonparametric regression function and finds that the MaxEnt process regression model includes the well-known Gaussian process regression (GPR) model as a special case. Then, this special MaxEnt process regression model, i.e., the GPR model, is generalized to obtain a robust sample-selection Gaussian process regression (RSGPR) model that deals with non-normal data in the sample selection. Various properties of the RSGPR model are established, including the stochastic representation, distributional hierarchy, and magnitude of the sample-selection bias. These properties are used in the paper to develop a hierarchical Bayesian methodology to estimate the model. This involves a simple and computationally feasible Markov chain Monte Carlo algorithm that avoids analytical or numerical derivatives of the log-likelihood function of the model. The performance of the RSGPR model in terms of the sample-selection bias correction, robustness to non-normality, and prediction, is demonstrated through results in simulations that attest to its good finite-sample performance. MDPI 2018-04-09 /pmc/articles/PMC7512777/ /pubmed/33265353 http://dx.doi.org/10.3390/e20040262 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Kim, Hea-Jung
Bae, Mihyang
Jin, Daehwa
On a Robust MaxEnt Process Regression Model with Sample-Selection
title On a Robust MaxEnt Process Regression Model with Sample-Selection
title_full On a Robust MaxEnt Process Regression Model with Sample-Selection
title_fullStr On a Robust MaxEnt Process Regression Model with Sample-Selection
title_full_unstemmed On a Robust MaxEnt Process Regression Model with Sample-Selection
title_short On a Robust MaxEnt Process Regression Model with Sample-Selection
title_sort on a robust maxent process regression model with sample-selection
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512777/
https://www.ncbi.nlm.nih.gov/pubmed/33265353
http://dx.doi.org/10.3390/e20040262
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