Estimation of sparse functional quantile regression with measurement error: a SIMEX approach
Carmen D Tekwe1, Mengli Zhang2, Raymond J Carroll3
1Department of Epidemiology and Biostatistics, Indiana University, Bloomington, IN 47405, USA.
Biostatistics (Oxford, England)
|May 31, 2022
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.
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.
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