1. Testing symmetry of model errors for non linear multiplicative distortion measurement error models.
- Author
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Zhang, Jun, Feng, Zhenghui, and Zhou, Yue
- Subjects
- *
MEASUREMENT errors , *ERRORS-in-variables models , *STATISTICAL correlation , *DISTRIBUTION (Probability theory) , *CHI-square distribution , *CHI-squared test , *INFERENTIAL statistics - Abstract
To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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