Robust estimation for varying-coefficient partially nonlinear model with nonignorable missing response

Yanting Xiao; Yifan Shi; Yanting Xiao; Yifan Shi

doi:10.3934/math.20231526

AIMS Mathematics

2023, Volume 8, Issue 12: 29849-29871. doi: 10.3934/math.20231526

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Robust estimation for varying-coefficient partially nonlinear model with nonignorable missing response

Yanting Xiao ^,,
Yifan Shi

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

Received: 21 August 2023 Revised: 24 September 2023 Accepted: 15 October 2023 Published: 02 November 2023
MSC : 62G10, 62G05

In this paper, we studied the robust estimation for the varying-coefficient partially nonlinear model based on modal regression with nonignorable missing response. First, an instrumental variable was used to handle the identifiability issue of parameters in the propensity score function, and a generalized method of moment was combined to obtain the consistent estimators. Second, inverse probability weighting and modal regression were adopted to construct the estimators of parameters and coefficient function in the model. Under some mild conditions, the asymptotic properties of the resulting estimators were established. Furthermore, simulation studies and a real example were carried out to illustrate the effectiveness of our proposed estimation procedures.
- varying-coefficient partially nonlinear model,
- nonignorable missing data,
- instrumental variable,
- modal regression,
- inverse probability weighting
Citation: Yanting Xiao, Yifan Shi. Robust estimation for varying-coefficient partially nonlinear model with nonignorable missing response[J]. AIMS Mathematics, 2023, 8(12): 29849-29871. doi: 10.3934/math.20231526

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Abstract

In this paper, we studied the robust estimation for the varying-coefficient partially nonlinear model based on modal regression with nonignorable missing response. First, an instrumental variable was used to handle the identifiability issue of parameters in the propensity score function, and a generalized method of moment was combined to obtain the consistent estimators. Second, inverse probability weighting and modal regression were adopted to construct the estimators of parameters and coefficient function in the model. Under some mild conditions, the asymptotic properties of the resulting estimators were established. Furthermore, simulation studies and a real example were carried out to illustrate the effectiveness of our proposed estimation procedures.

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