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On function-on-function linear quantile regression.

Muge Mutis1, Ufuk Beyaztas2, Filiz Karaman1

  • 1Department of Statistics, Yildiz Technical University, Esenler-Istanbul, Turkiye.

Journal of Applied Statistics
|March 5, 2025
PubMed
Summary
This summary is machine-generated.

We developed new functional partial quantile regression algorithms for accurate function-on-function linear quantile regression. These methods efficiently estimate coefficient functions, outperforming existing techniques in simulations and real-world data analysis.

Keywords:
Basis expansion functionsfunction-on-function linear quantile regressionfunctional partial least squares regressionquantile covariancequantile regression

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Area of Science:

  • Statistics
  • Econometrics
  • Functional Data Analysis

Background:

  • Functional data analysis (FDA) involves data where observations are functions.
  • Function-on-function regression models relationships between functions.
  • Quantile regression provides a more comprehensive analysis than mean regression by estimating conditional quantiles.

Purpose of the Study:

  • To introduce two novel algorithms for functional partial quantile regression.
  • To accurately and efficiently estimate the regression coefficient function in function-on-function linear quantile regression models.
  • To address the challenge of infinite-dimensional data in functional regression.

Main Methods:

  • Functional partial quantile regression decomposition to reduce dimensionality.
  • Basis expansion for approximating partial quantile regression components.
  • Approximation of infinite-dimensional models using multivariate quantile regression.

Main Results:

  • The proposed algorithms demonstrate superior performance in finite-sample scenarios.
  • Empirical results show improved accuracy and efficiency compared to existing methods.
  • Successful implementation in the R package ffpqr.

Conclusions:

  • The developed algorithms provide an effective approach for functional partial quantile regression.
  • These methods offer a valuable tool for analyzing complex functional data.
  • The ffpqr package facilitates the application of these advanced statistical techniques.