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August 2020 Calibration procedures for linear regression models with multiplicative distortion measurement errors
Jun Zhang, Yan Zhou
Braz. J. Probab. Stat. 34(3): 519-536 (August 2020). DOI: 10.1214/19-BJPS451


This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. To eliminate the effect caused by the distortion, we propose two calibration procedures: the conditional absolute mean calibration and the conditional variance calibration. Both calibration procedures avoid using the nonzero expectation conditions imposed on the variables in the literature. Utilizing these calibrated variables, the least squares estimators are obtained, associated with their asymptotic results. The asymptotic normal confidence intervals and empirical likelihood confidence intervals are also proposed. Simulation studies are conducted to compare the proposed calibration procedures and a real example is analyzed to illustrate our proposed method.


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Jun Zhang. Yan Zhou. "Calibration procedures for linear regression models with multiplicative distortion measurement errors." Braz. J. Probab. Stat. 34 (3) 519 - 536, August 2020.


Received: 1 February 2019; Accepted: 1 June 2019; Published: August 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07232911
MathSciNet: MR4124539
Digital Object Identifier: 10.1214/19-BJPS451

Keywords: Calibration , confidence intervals , least squares estimator , local linear smoothing , Measurement errors , multiplicative distortion

Rights: Copyright © 2020 Brazilian Statistical Association


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Vol.34 • No. 3 • August 2020
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