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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Semiparametric varying coefficient models are widely used in various fields.
  • Challenges arise when the covariate modifying coefficients is functional and requires nonparametric modeling.
  • Existing methods may lack efficiency or theoretical guarantees for such complex models.

Purpose of the Study:

  • To develop and analyze novel estimation techniques for semiparametric varying coefficient models with functional covariates.
  • To provide theoretical guarantees for the proposed estimators.
  • To demonstrate the practical utility of the methodology through simulations and real-world data.

Main Methods:

  • Kernel-based estimation for the nonparametric functional component.
  • Profiling estimation for the parametric component.
  • Derivation of asymptotic properties, including consistency and asymptotic expansion.

Main Results:

  • The proposed kernel-based estimator demonstrates consistency for the nonparametric functional estimates.
  • The profiling estimator yields asymptotic expansions for the parametric component estimates.
  • The methodology shows robust performance in simulation studies and a real data application.

Conclusions:

  • The developed methods offer a statistically sound and practically applicable approach for semiparametric varying coefficient models with functional covariates.
  • The theoretical results provide confidence in the reliability of the estimators.
  • This work contributes to the advancement of statistical modeling techniques in data analysis.