On a Robust MaxEnt Process Regression Model with Sample-Selection

被引:7
|
作者
Kim, Hea-Jung [1 ]
Bae, Mihyang [1 ]
Jin, Daehwa [1 ]
机构
[1] Dongguk Univ Seoul, Dept Stat, Pil Dong 3Ga, Seoul 100715, South Korea
来源
ENTROPY | 2018年 / 20卷 / 04期
基金
新加坡国家研究基金会;
关键词
Gaussian process model; hierarchical Bayesian methodology; robust sample-selection MaxEnt process regression model; Markov chain Monte Carlo; sample-selection bias; bias collection; SCALE MIXTURES; NORMAL-DISTRIBUTIONS; INFERENCE; CONSTRAINT; ERROR;
D O I
10.3390/e20040262
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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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页数:19
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