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March 2020 Learning Semiparametric Regression with Missing Covariates Using Gaussian Process Models
Abhishek Bishoyi, Xiaojing Wang, Dipak K. Dey
Bayesian Anal. 15(1): 215-239 (March 2020). DOI: 10.1214/18-BA1136

Abstract

Missing data often appear as a practical problem while applying classical models in the statistical analysis. In this paper, we consider a semiparametric regression model in the presence of missing covariates for nonparametric components under a Bayesian framework. As it is known that Gaussian processes are a popular tool in nonparametric regression because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. However, in the absence of covariates, the most frequently used covariance functions of a Gaussian process will not be well defined. We propose an imputation method to solve this issue and perform our analysis using Bayesian inference, where we specify the objective priors on the parameters of Gaussian process models. Several simulations are conducted to illustrate effectiveness of our proposed method and further, our method is exemplified via two real datasets, one through Langmuir equation, commonly used in pharmacokinetic models, and another through Auto-mpg data taken from the StatLib library.

Citation

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Abhishek Bishoyi. Xiaojing Wang. Dipak K. Dey. "Learning Semiparametric Regression with Missing Covariates Using Gaussian Process Models." Bayesian Anal. 15 (1) 215 - 239, March 2020. https://doi.org/10.1214/18-BA1136

Information

Published: March 2020
First available in Project Euclid: 9 April 2019

zbMATH: 1437.62137
MathSciNet: MR4050883
Digital Object Identifier: 10.1214/18-BA1136

Subjects:
Primary: 60K35, 60K35
Secondary: 60K35

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Vol.15 • No. 1 • March 2020
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