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

Jun Zhang ()
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Jun Zhang: Institute of Statistical Sciences, Shenzhen University

Statistical Papers, 2021, vol. 62, issue 2, No 14, 887-913

Abstract: 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.

Keywords: Calibration; Local linear smoothing; Profile least squared estimator; Multiplicative distortion measurement errors; 62G05; 62G08; 62G20 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-019-01119-6

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