Abstract
In this paper, we investigate the least squares (LS) estimator of the nonlinear regression model based on the extended negatively dependent errors which are widely dependent structures. Under the general conditions, we establish some large deviation results for the LS estimator of the nonlinear regression parameter, which can be applied to obtain a weak uniform consistency and a complete convergence rate for this estimator. In addition, some examples and simulations are presented for illustration.
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Acknowledgements
The authors are deeply grateful to the editor, the associate editor and three anonymous referees for their careful reading and insightful comments. The comments led us to significantly improve the paper. This work is supported by the National Natural Science Foundation of China (Grant: 11426032, 11501005, 11526033, 11671012), National Social Science Fund of China (Grant: 14ATJ005), Natural Science Foundation of Anhui Province (Grant: 1408085QA02, 1508085J06, 1608085QA02), Provincial Natural Science Research Project of Anhui Colleges (Grant: KJ2014A020, KJ2015A065, KJ2016A027), Quality Engineering Project of Anhui Province (2015jyxm054) and Applied Teaching Model Curriculum of Anhui University (XJYYKC1401, ZLTS2015053).
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Yang, W., Zhao, Z., Wang, X. et al. The large deviation results for the nonlinear regression model with dependent errors. TEST 26, 261–283 (2017). https://doi.org/10.1007/s11749-016-0509-z
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DOI: https://doi.org/10.1007/s11749-016-0509-z