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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| Language: | English |
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MDPI AG
2018-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/4/262 |
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| author | Hea-Jung Kim Mihyang Bae Daehwa Jin |
| author_facet | Hea-Jung Kim Mihyang Bae Daehwa Jin |
| author_sort | Hea-Jung Kim |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T18:02:16Z |
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| id | doaj.art-a2cb99ff5e1245ceb73a89abb3cd46d2 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T18:02:16Z |
| publishDate | 2018-04-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-a2cb99ff5e1245ceb73a89abb3cd46d22022-12-22T04:10:26ZengMDPI AGEntropy1099-43002018-04-0120426210.3390/e20040262e20040262On a Robust MaxEnt Process Regression Model with Sample-SelectionHea-Jung Kim0Mihyang Bae1Daehwa Jin2Department of Statistics, Dongguk University-Seoul, Pil-Dong 3Ga, Chung-Gu, Seoul 100-715, KoreaDepartment of Statistics, Dongguk University-Seoul, Pil-Dong 3Ga, Chung-Gu, Seoul 100-715, KoreaDepartment of Statistics, Dongguk University-Seoul, Pil-Dong 3Ga, Chung-Gu, Seoul 100-715, KoreaIn 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.http://www.mdpi.com/1099-4300/20/4/262Gaussian process modelhierarchical Bayesian methodologyrobust sample-selection MaxEnt process regression modelMarkov chain Monte Carlosample-selection biasbias correction |
| spellingShingle | Hea-Jung Kim Mihyang Bae Daehwa Jin On a Robust MaxEnt Process Regression Model with Sample-Selection Entropy Gaussian process model hierarchical Bayesian methodology robust sample-selection MaxEnt process regression model Markov chain Monte Carlo sample-selection bias bias correction |
| 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 | Gaussian process model hierarchical Bayesian methodology robust sample-selection MaxEnt process regression model Markov chain Monte Carlo sample-selection bias bias correction |
| url | http://www.mdpi.com/1099-4300/20/4/262 |
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