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Locally sparse quantile estimation for a partially functional interaction model.

Weijuan Liang1, Qingzhao Zhang2, Shuangge Ma3

  • 1School of Statistics, Renmin University of China, Beijing, China.

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|November 18, 2024
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Summary
This summary is machine-generated.

This study introduces a new statistical model for analyzing data with both scalar and functional variables, including their interactions. The proposed method effectively handles complex error distributions and identifies important effects for better interpretation.

Keywords:
Interaction analysisLocally sparse estimationPartially functional modelQuantile estimation

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Econometrics

Background:

  • Functional data analysis is widely used.
  • Existing models often assume simple error distributions and do not fully capture complex interactions.
  • Partially functional models with scalar and functional covariates are gaining traction.

Purpose of the Study:

  • To develop a novel partially functional model incorporating interactions between scalar and functional covariates.
  • To address challenges posed by long-tailed error distributions and achieve interpretable estimation.
  • To introduce a method that respects the main effect-interaction hierarchy and performs variable selection.

Main Methods:

  • A partially functional model with linear scalar effects and nonlinear functional effects.
  • Quantile regression for handling long-tailed error distributions.
  • A penalization approach for estimation, local sparsity identification, and hierarchy adherence.
  • Development of an effective computational algorithm.

Main Results:

  • The proposed penalization approach effectively estimates model parameters and identifies local sparsity.
  • Consistency properties of the estimation method are rigorously established under mild conditions.
  • Simulation studies demonstrate the practical effectiveness of the approach.

Conclusions:

  • The study presents a novel and practically useful partially functional model with interaction terms.
  • The proposed estimation approach is statistically sound and numerically efficient.
  • The method is applicable to real-world data, as shown by the Tecator data analysis.