Detection of the symmetry of model errors for partial linear single-index models

Gai, Yujie; Zhang, Jun

doi:10.1080/03610918.2020.1752381

Cited by 2 publications

(2 citation statements)

References 62 publications

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“…The asymptotic result of η0.5 is similar to the asymptotic results in Zhang et al ( 2018); Gai and Zhang (2022b); ; Gai and Zhang (2022a); Gai, Zhu, and Zhang (2022), but the asymptotic variances are more complicated with extra asymptotic matrix or variance related with distortion functions φ(u) and ψ r (u)'s. As Partlett and Patil (2017) claimed, a numerical method is needed to evaluate the integrals such as 2022); Gai and Zhang (2022a); Gai, Zhu, and Zhang (2022) suggested using the empirical likelihood method to construct the confidence intervals, or equivalently, the test statistics when the null hypothesis H 0 holds.…”

Section: Conditional Mean Calibrationsupporting

confidence: 81%

“…). This measure η k coupling with empirical likelihood method is further used to check the symmetry of model errors in various semiparametric regression models, and readers can refer to Gai and Zhang (2022b); ; Gai and Zhang (2022a); Gai, Zhu, and Zhang (2022). In these studies, researchers find that the empirical likelihood test statistics by taking k = 0.5 usually perform the best when the sample size is large.…”

Section: Testing Symmetry Of the Error Distributionmentioning

confidence: 99%

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Testing symmetry of model errors for non linear multiplicative distortion measurement error models

Zhang,

Feng,

Zhou

2023

Communications in Statistics - Theory and Methods

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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 calibrationbased residuals, and the conditional absolute logarithmic calibrationbased 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.

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Section: Conditional Mean Calibrationsupporting

confidence: 81%