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LPRE estimation for functional multiplicative model and optimal subsampling.

Qian Yan1, Hanyu Li1

  • 1College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic China.

Journal of Applied Statistics
|December 4, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a functional linear multiplicative model using a novel error criterion. It establishes estimator consistency and develops optimal subsampling techniques for large datasets, enhancing statistical efficiency.

Keywords:
Least product relative errorasymptotic normalityfunctional multiplicative modelmassive dataoptimal subsampling

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • The functional linear multiplicative model is crucial for analyzing complex data structures.
  • Existing methods may lack efficiency when dealing with massive datasets.
  • The least product relative error criterion offers a robust alternative for model fitting.

Purpose of the Study:

  • To investigate the functional linear multiplicative model using the least product relative error criterion.
  • To establish theoretical properties of the estimator, including consistency and asymptotic normality.
  • To develop and evaluate optimal subsampling strategies for handling massive data in this model.

Main Methods:

  • Establishing consistency and asymptotic normality of the estimator under regularization conditions.
  • Deriving the consistency and asymptotic distribution of the subsampling estimator.
  • Determining optimal subsampling probabilities via the A-optimality criterion.
  • Proposing practical alternative subsampling probabilities that avoid Hessian matrix inversion.

Main Results:

  • Theoretical guarantees for the consistency and asymptotic normality of the primary estimator.
  • Demonstrated consistency and derived asymptotic distribution for the subsampling estimator.
  • Identification of optimal and practical subsampling probabilities for large-scale applications.
  • Validation of proposed methods through numerical simulations and real-world data analysis.

Conclusions:

  • The proposed least product relative error approach provides a consistent and asymptotically normal estimator for the functional linear multiplicative model.
  • Optimal subsampling strategies significantly improve efficiency for massive datasets.
  • The alternative subsampling probabilities offer a computationally feasible and effective solution for practical implementation.