Linear regression models with multiplicative distortions under new identifiability conditions

Author:

Zhang Jun1ORCID,Lin Bingqing1,Zhou Yan1

Affiliation:

1. College of Mathematics and Statistics Shenzhen University Shenzhen China

Abstract

This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. We propose new identifiability conditions for the distortion functions via the varying coefficient models, then moment‐based estimators of parameters in the model are proposed by using the estimated varying coefficient functions. This method does not require the independence condition between the confounding variables and the unobserved response and variables. We establish the connections among the varying coefficient based estimators, the conditional mean calibration and the conditional absolute mean calibration. We study the asymptotic results of these proposed estimators, and discuss their asymptotic efficiencies. Lastly, we make some comparisons among the proposed estimators through the simulation. These methods are applied to analyze a real dataset for an illustration.

Funder

National Natural Science Foundation of China

Publisher

Wiley

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Covariance ratio under multiplicative distortion measurement errors;Communications in Statistics - Theory and Methods;2023-12-25

2. Estimation of correlation coefficient with monotone transformation and multiplicative distortions;Communications in Statistics - Theory and Methods;2023-12-09

3. Non parametric regression models with additive distortions;Communications in Statistics - Theory and Methods;2023-11-21

4. Parametric hypothesis tests for exponentiality under multiplicative distortion measurement errors data;Communications in Statistics - Simulation and Computation;2023-07-24

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