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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zhensheng Huang & Xing Sun & Riquan Zhang, 2022. "Estimation for partially varying-coefficient single-index models with distorted measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 175-201, February.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:2:d:10.1007_s00184-021-00823-4
    DOI: 10.1007/s00184-021-00823-4
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    References listed on IDEAS

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