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Statistics in Medicine
Article . 2023 . Peer-reviewed
License: CC BY NC ND
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zbMATH Open
Article . 2023
Data sources: zbMATH Open
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Joint semiparametric kernel network regression

Authors: Byung‐Jun Kim; Inyoung Kim;

Joint semiparametric kernel network regression

Abstract

Variable selection and graphical modeling play essential roles in highly correlated and high‐dimensional (HCHD) data analysis. Variable selection methods have been developed under both parametric and nonparametric model settings. However, variable selection for nonadditive, nonparametric regression with high‐dimensional variables is challenging due to complications in modeling unknown dependence structures among HCHD variables. Gaussian graphical models are a popular and useful tool for investigating the conditional dependence between variables via estimating sparse precision matrices. For a given class of interest, the estimated precision matrices can be mapped onto networks for visualization. However, the limitation of Gaussian graphical models is that they are only applicable to discretized response variables and for the case when , where is the number of variables and is the sample size. They are necessary to develop a joint method for variable selection and graphical modeling. To the best of our knowledge, the methods for simultaneously selecting variable selection and estimating networks among variables in the semiparametric regression settings are quite limited. Hence, in this paper, we develop a joint semiparametric kernel network regression method to solve this limitation and to provide a connection between them. Our approach is a unified and integrated method that can simultaneously identify important variables and build a network among those variables. We developed our approach under a semiparametric kernel machine regression framework, which can allow for nonlinear or nonadditive associations and complicated interactions among the variables. The advantages of our approach are that it can (1) simultaneously select variables and build a network among HCHD variables under a regression setting; (2) model unknown and complicated interactions among the variables and estimate the network among these variables; (3) allow for any form of semiparametric model, including non‐additive, nonparametric model; and (4) provide an interpretable network that considers important variables and a response variable. We demonstrate our approach using a simulation study and real application on genetic pathway‐based analysis.

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Keywords

semiparametric model, Sample Size, least square kernel machine, Humans, Regression Analysis, graphical model, Computer Simulation, Applications of statistics to biology and medical sciences; meta analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
hybrid