Estimation for partially varying-coefficient single-index models with distorted measurement errors

Zhensheng Huang (), Xing Sun and Riquan Zhang
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Zhensheng Huang: Nanjing University of Science and Technology
Xing Sun: Nanjing University of Science and Technology
Riquan Zhang: Key Laboratory of Advanced Theory and Application in Statistics and Data Science—MOE, East China Normal University

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 2, No 2, 175-201

Abstract: Abstract In this paper, we study partially varying-coefficient single-index model where both the response and predictors are observed with multiplicative distortions which depend on a commonly observable confounding variable. Due to the existence of measurement errors, the existing methods cannot be directly applied, so we recommend using the nonparametric regression to estimate the distortion functions and obtain the calibrated variables accordingly. With these corrected variables, the initial estimators of unknown coefficient and link functions are estimated by assuming that the parameter vector $$\beta $$ β is known. Furthermore, we can obtain the least square estimators of unknown parameters. Moreover, we establish the asymptotic properties of the proposed estimators. Simulation studies and real data analysis are given to illustrate the advantage of our proposed method.

Keywords: Distorted measurement errors; Profile nonlinear least square method; Single-index model; Varying-coefficient model (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00823-4

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