Robust estimation for varying-coefficient partially linear measurement error model with auxiliary instrumental variables

Yanting Xiao; Wanying Dong; Yanting Xiao; Wanying Dong

doi:10.3934/math.2023934

AIMS Mathematics

2023, Volume 8, Issue 8: 18373-18391. doi: 10.3934/math.2023934

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Research article

Robust estimation for varying-coefficient partially linear measurement error model with auxiliary instrumental variables

Yanting Xiao ^,,
Wanying Dong

Department of Applied Mathematics, Xi'an University of Technology, Xi'an, Shaanxi 710048, China

Received: 01 March 2023 Revised: 31 March 2023 Accepted: 17 April 2023 Published: 29 May 2023
MSC : 62G10, 62G05

We study the varying-coefficient partially linear model when some linear covariates are not observed, but their auxiliary instrumental variables are available. Combining the calibrated error-prone covariates and modal regression, we present a two-stage efficient estimation procedure, which is robust against outliers or heavy-tail error distributions. Asymptotic properties of the resulting estimators are established. Performance of our proposed estimation procedure is illustrated through some numerous simulations and a real example. And the results confirm that the proposed methods are satisfactory.
- varying-coefficient partially linear models,
- auxiliary variables,
- error-in-variable,
- modal regression
Citation: Yanting Xiao, Wanying Dong. Robust estimation for varying-coefficient partially linear measurement error model with auxiliary instrumental variables[J]. AIMS Mathematics, 2023, 8(8): 18373-18391. doi: 10.3934/math.2023934

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Abstract

We study the varying-coefficient partially linear model when some linear covariates are not observed, but their auxiliary instrumental variables are available. Combining the calibrated error-prone covariates and modal regression, we present a two-stage efficient estimation procedure, which is robust against outliers or heavy-tail error distributions. Asymptotic properties of the resulting estimators are established. Performance of our proposed estimation procedure is illustrated through some numerous simulations and a real example. And the results confirm that the proposed methods are satisfactory.

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