Abstract
The second-order least-squares estimator (SLSE) was proposed by Wang (Statistica Sinica 13:1201–1210, 2003) for measurement error models. It was extended and applied to linear and nonlinear regression models by Abarin and Wang (Far East J Theor Stat 20:179–196, 2006) and Wang and Leblanc (Ann Inst Stat Math 60:883–900, 2008). The SLSE is asymptotically more efficient than the ordinary least-squares estimator if the error distribution has a nonzero third moment. However, it lacks robustness against outliers in the data. In this paper, we propose a robust second-order least squares estimator (RSLSE) against X-outliers. The RSLSE is highly efficient with high breakdown point and is asymptotically normally distributed. We compare the RSLSE with other estimators through a simulation study. Our results show that the RSLSE performs very well.
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Chen, X., Tsao, M. & Zhou, J. Robust second-order least-squares estimator for regression models. Stat Papers 53, 371–386 (2012). https://doi.org/10.1007/s00362-010-0343-4
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DOI: https://doi.org/10.1007/s00362-010-0343-4
Keywords
- Breakdown point
- High efficiency
- Influence function
- Linear regression
- Outliers
- Robust estimation
- Second-order least-squares estimator