ABSTRACT 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.

中文翻译：

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具有乘性失真测量误差的部分线性模型的对数校准

摘要在本文中，当参数部分中的响应变量和协变量都不能直接观察时，我们通过对乘法失真部分线性测量误差模型使用对数校准提出了一种新的可识别条件。我们为未观察到的变量提出了对数校准估计程序。然后，提出了轮廓最小二乘估计器，与其渐近结果和置信区间构造相关联。对于参数的假设检验，提出了原假设下的受限估计量和检验统计量。还建立了估计量和检验统计量的渐近特性。我们采用平滑剪裁的绝对偏差惩罚来选择相关变量。