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Estimation and variable selection for partial linear single-index distortion measurement errors models

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  • Jun Zhang

    (Institute of Statistical Sciences, Shenzhen University)

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.

Suggested Citation

  • Jun Zhang, 2021. "Estimation and variable selection for partial linear single-index distortion measurement errors models," Statistical Papers, Springer, vol. 62(2), pages 887-913, April.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01119-6
    DOI: 10.1007/s00362-019-01119-6
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    References listed on IDEAS

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    Cited by:

    1. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.

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