Multiplicative regression models with distortion measurement errors

Jun Zhang, Junpeng Zhu, Yan Zhou (), Xia Cui and Tao Lu
Additional contact information
Jun Zhang: Shenzhen University
Junpeng Zhu: Shenzhen University
Yan Zhou: Shenzhen University
Xia Cui: Guangzhou University
Tao Lu: University of Nevada

Statistical Papers, 2020, vol. 61, issue 5, No 12, 2057 pages

Abstract: Abstract This paper considers estimation and variable selection for multiplicative linear regression models when neither the response variable nor the covariates can be directly observed, but are distorted by unknown functions of a commonly observable confounding variable. After taking logarithmic transformation on the response variable, we propose two estimation methods for the parameter. One is the least squares estimator, the second one is the moment-based estimator linked with varying coefficient models. The third one is the least product relative error estimator without logarithmic transformation. For the hypothesis testing of parametric components, restricted estimators under the null hypothesis and test statistics are proposed. The asymptotic properties for the estimators and test statistics are established. A bootstrap procedure is proposed to calculate critical values. 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: Distortion measurement errors; Local linear smoothing; Varying coefficient models; Least product relative error estimator; Variable selection; 62G05; 62G08; 62G20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00362-018-1020-2

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