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On a Robust MaxEnt Process Regression Model with Sample-Selection

Department of Statistics, Dongguk University-Seoul, Pil-Dong 3Ga, Chung-Gu, Seoul 100-715, Korea
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Entropy 2018, 20(4), 262; https://doi.org/10.3390/e20040262
Received: 2 February 2018 / Revised: 3 April 2018 / Accepted: 7 April 2018 / Published: 9 April 2018
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. View Full-Text
Keywords: Gaussian process model; hierarchical Bayesian methodology; robust sample-selection MaxEnt process regression model; Markov chain Monte Carlo; sample-selection bias; bias correction Gaussian process model; hierarchical Bayesian methodology; robust sample-selection MaxEnt process regression model; Markov chain Monte Carlo; sample-selection bias; bias correction
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Kim, H.-J.; Bae, M.; Jin, D. On a Robust MaxEnt Process Regression Model with Sample-Selection. Entropy 2018, 20, 262.

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