Abstract
This paper considers partial linear single-index regression models when all the variables are measured with multiplicative distortion measurement errors. To eliminate the effect caused by the distortion, we propose the conditional absolute mean calibration. This method avoids to use the nonzero expectation conditions imposed on the variables in the literature. Using the calibrated variables, a profile least squares estimator is obtained. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. A smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.
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Acknowledgements
The authors thank the editor, the associate editor, and a referee for their constructive suggestions that helped us to improve the early manuscript. Jun Zhang’s research was supported by the National Natural Science Foundation of China (Grant No. 11871411).
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Zhang, J. Estimation and variable selection for partial linear single-index distortion measurement errors models. Stat Papers 62, 887–913 (2021). https://doi.org/10.1007/s00362-019-01119-6
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DOI: https://doi.org/10.1007/s00362-019-01119-6
Keywords
- Calibration
- Local linear smoothing
- Profile least squared estimator
- Multiplicative distortion measurement errors