Logarithmic calibration for multiplicative distortion measurement errors regression models |
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Authors: | Jun Zhang Yiping Yang Gaorong Li |
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Affiliation: | 1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, China;2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China;3. School of Statistics, Beijing Normal University, Beijing, 100875 China |
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Abstract: | In this article, we propose a new identifiability condition by using the logarithmic calibration for the distortion measurement error models, where neither the response variable nor the covariates can be directly observed but are measured with multiplicative measurement errors. Under the logarithmic calibration, the direct-plug-in estimators of parameters and empirical likelihood based confidence intervals are proposed, and we studied the asymptotic properties of the proposed estimators. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the restricted estimator and test statistic are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage. |
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Keywords: | local linear smoothing logarithmic calibration measurement errors multiplicative distortion |
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