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Quadratic inference with dense functional responses.

Pratim Guha Niyogi1, Ping-Shou Zhong2

  • 1Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Maryland, USA.

Journal of Multivariate Analysis
|August 6, 2025
PubMed
Summary
This summary is machine-generated.

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This study introduces a novel quadratic inference approach for estimating constant linear effect models with dense functional responses. The method offers improved estimation accuracy and asymptotic normality, outperforming existing techniques in simulations and real-world data analysis.

Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Constant linear effect models with dense functional responses present estimation challenges.
  • Existing methods may require specific correlation structure assumptions.

Purpose of the Study:

  • To develop an alternative estimation method for constant linear effect models with dense functional responses.
  • To leverage the quadratic inference approach for robust coefficient estimation.

Main Methods:

  • Utilizing the quadratic inference approach for regression coefficient estimation.
  • Employing non-parametrically estimated basis functions to avoid specifying correlation structures.
  • Analyzing correlated functional data.

Main Results:

Keywords:
Constant Linear-Effect ModelsFunctional Principal Component AnalysisQuadratic InferenceSemi-parametric Functional Regression

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  • Achieving a parametric sqrt(n)-convergence rate under specific bandwidth and data conditions.
  • Establishing the asymptotic normality of the proposed estimator.
  • Demonstrating superior performance compared to existing methods via simulations.

    • Conclusions:

    • The proposed quadratic inference method provides an effective and robust solution for functional response models.
    • The method achieves desirable convergence rates and asymptotic properties.
    • Validated through simulations and real data analysis, showing practical utility.