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PARTIALLY FUNCTIONAL LINEAR QUANTILE REGRESSION WITH MEASUREMENT ERRORS.

Mengli Zhang1, Lan Xue2, Carmen D Tekwe3

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|August 27, 2024
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Summary
This summary is machine-generated.

This study introduces a new method to correct bias in regression analysis caused by measurement errors in functional data. The proposed technique improves estimation accuracy for functional coefficient models, particularly in areas like child obesity research.

Keywords:
Corrected scorefunctional measurement errorfunctional principle componentphysical activityquantile regressionwearable devices

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Area of Science:

  • Statistics
  • Biostatistics
  • Functional Data Analysis

Background:

  • Measurement errors in covariates can bias regression results.
  • Correcting bias is difficult when covariates are functional curves.
  • Existing methods may not adequately address functional measurement errors.

Purpose of the Study:

  • To propose a novel corrected loss function for partially functional linear quantile models.
  • To address function-valued measurement errors in covariates.
  • To reduce bias in estimation and inference for functional regression.

Main Methods:

  • Development of a new corrected loss function.
  • Analysis of asymptotic properties for functional and parametric coefficient estimators.
  • Application to a partially functional linear quantile model framework.

Main Results:

  • The proposed method provides corrected estimation for functional coefficients.
  • Asymptotic properties of estimators are established.
  • Simulation studies confirm finite-sample performance.

Conclusions:

  • The new corrected loss function effectively reduces bias in functional regression with measurement errors.
  • The method demonstrates practical advantages in real-world data analysis, such as in child obesity studies.