Logarithmic calibration for partial linear models with multiplicative distortion measurement errors

In this paper, we propose a new identifiability condition by using the logarithmic calibration for the multiplicative distortion partial linear measurement errors models, when neither the response variable nor the covariates in the parametric part can be directly observed. We propose a logarithmic calibration estimation procedure for the unobserved variables. Then, a profile least squares estimator is proposed, associated with its asymptotic results and confidence intervals construction. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the estimator and test statistic are also established. We employ the smoothly clipped absolute deviation penalty to select relevant variables. Simulation studies demonstrate the performance of the proposed procedure and a real example is analysed to illustrate its practical usage.