Abstract
In the paper, an exponential inequality for widely orthant dependent random variables is established without bounded condition. By using the inequality, we further investigate the strong linear representation for the M estimator of the regression parameter vector in linear regression models with widely orthant dependent random errors under some general conditions. In addition, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.
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Acknowledgements
The study was supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005), The Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123) and the Science Research Project of Anhui Colleges (KJ2017A027).
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Deng, X., Wang, X. An exponential inequality and its application to M estimators in multiple linear models. Stat Papers 61, 1607–1627 (2020). https://doi.org/10.1007/s00362-018-0994-0
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DOI: https://doi.org/10.1007/s00362-018-0994-0
Keywords
- Exponential inequality
- Strong linear representation
- M estimator
- Linear regression model
- Widely orthant dependent random variables