Correlation curve estimation for multiplicative distortion measurement errors data

Nonparametric Additive Distortion Measurement Errors Models

“…Remark The asymptotic bias term η(x) is the same as Proposition 2.1(b) in Feng, Gai and Zhang (2019). And (κ ′ I (x), κ ′ II (x)) are the first-order derivative of (κ…”

“…Roughly, ρ(x) represents the variance explained by the regression model divided by the total variance. When (Y, X) is distorted and observed with multiplicative measurement errors in model (1.1), there is only one literature Feng, Gai and Zhang (2019). In this section, we will study the asymptotic behavior when the additive distortion measurement error exists in the model.…”

Linear regression models with multiplicative distortions under new identifiability conditions

“…Thus, the condition $$$ E\left(|Y|\right){\prod}_{k=1}^qE\left(|{X}_k|\right)\ne 0 $$$ is more mild and less restrict than $$$ E(Y){\prod}_{k=1}^qE\left({X}_k\right)\ne 0 $$$. Recent research about the conditional absolute mean calibration methods, readers can refer to Zhao and Xie (2018); Zhang and Zhou (2020); Feng et al (2019); Zhang et al (2022); Zhang, Lin, and Feng (2020); Zhang, Gai, Cui, and Li (2020); Zhang (2021); Zhang, Zhu, Zhou, et al (2020); Zhang, Chen, and Wei (2023).…”

“…conditions in the literature, such as the "no average distortions" in the original covariates (Feng, Gai, & Zhang, 2019;Li, Zhang, & Feng, 2016;Şentürk & Müller, 2005a;Şentürk & Müller, 2006;Zhang, 2019Zhang, , 2021Zhang, , 2022Zhang, Gai, Cui, & Li, 2020;Zhang, Li, & Yang, 2022;Zhang, Lin, & Feng, 2020;Zhang, Zhu, Zhou, et al, 2020;Zhao & Xie, 2018;Zhou & Zhang, 2022) or in transformed covariates with logarithmic calibration (Zhang & Cui, 2021;Zhang, Yang, Feng, & Wei, 2020;Zhang, Yang, & Li, 2020). In these literature, the "no average distortion" conditions for covariates X are assumed that E[𝜓 k (U)] = 1, k = 1, … , q.…”