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Estimation of sparse functional quantile regression with measurement error: a SIMEX approach.

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Summary

This study introduces a new method to fix bias in quantile regression caused by measurement errors in functional covariates. The approach uses instrumental variables and simulation extrapolation (SIMEX) for accurate analysis.

Keywords:
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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Quantile regression models associations between variables, offering robustness to distributional assumptions and outliers.
  • Measurement error in covariates can bias quantile regression results, particularly for complex functional covariates.
  • Existing methods primarily address scalar-valued covariates, leaving functional covariates with heteroscedastic error unexamined.

Purpose of the Study:

  • To develop a robust statistical method for linear quantile regression with function-valued covariates affected by measurement error.
  • To address the impact of heteroscedastic error in function-valued covariates within quantile regression frameworks.
  • To provide a consistent estimation strategy for modeling relationships when functional predictors are measured with error.

Main Methods:

  • A two-stage strategy combining instrumental variables and simulation extrapolation (SIMEX).
  • Stage one: Instrumental variables estimate the measurement error covariance matrix.
  • Stage two: SIMEX corrects for measurement error in function-valued covariates; nonparametric bootstrap estimates standard errors.

Main Results:

  • Simulation studies demonstrate the robustness of the proposed measurement error correction method for functional quantile regression.
  • The developed method provides consistent estimates for models with functional covariates contaminated by measurement error.
  • Application to National Health and Examination Survey data assesses the physical activity-body mass index relationship in US adults.

Conclusions:

  • The proposed two-stage method effectively corrects for measurement error in function-valued covariates in quantile regression.
  • This approach enhances the reliability of statistical modeling when dealing with complex, error-prone functional predictors.
  • The findings have implications for epidemiological studies, such as analyzing the link between physical activity and BMI.