Orthogonality based modal empirical likelihood inferences for partially nonlinear models

Jieqiong Lu; Peixin Zhao; Xiaoshuang Zhou; Jieqiong Lu; Peixin Zhao; Xiaoshuang Zhou

doi:10.3934/math.2024884

AIMS Mathematics

2024, Volume 9, Issue 7: 18117-18133. doi: 10.3934/math.2024884

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Research article

Orthogonality based modal empirical likelihood inferences for partially nonlinear models

1.
School of Mathematics and Statistics, Shandong University of Technology, Shandong, Zibo 255000, China
2.
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
3.
College of Mathematics and Big Data, Dezhou University, Shandong, Dezhou 253600, China

Received: 22 March 2024 Revised: 08 May 2024 Accepted: 22 May 2024 Published: 29 May 2024
MSC : 62G05, 62G20

This paper explored the effective empirical likelihood inferences for partially nonlinear models. By combining the modal regression method with orthogonal projection technology, a modal empirical likelihood-based estimation procedure was proposed. The proposed empirical likelihood approach retained Wilk's theorem under mild conditions, and the confidence regions of model coefficients were constructed. Nonparametric and parametric components of the estimators were independent. Simulation results demonstrated that it is more robust and effective than the existing methods.
- partially nonlinear model,
- modal regression,
- empirical likelihood,
- orthogonality estimation
Citation: Jieqiong Lu, Peixin Zhao, Xiaoshuang Zhou. Orthogonality based modal empirical likelihood inferences for partially nonlinear models[J]. AIMS Mathematics, 2024, 9(7): 18117-18133. doi: 10.3934/math.2024884

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Abstract

This paper explored the effective empirical likelihood inferences for partially nonlinear models. By combining the modal regression method with orthogonal projection technology, a modal empirical likelihood-based estimation procedure was proposed. The proposed empirical likelihood approach retained Wilk's theorem under mild conditions, and the confidence regions of model coefficients were constructed. Nonparametric and parametric components of the estimators were independent. Simulation results demonstrated that it is more robust and effective than the existing methods.

References

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