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Effective sample preparation is crucial for accurate and reliable laboratory analysis. During this process, two significant sources of error can arise: concentration bias from improper sample splitting and contamination caused by methods used to reduce particle size, such as grinding or homogenization. Identifying and minimizing these potential errors is crucial to ensuring the validity of the analysis.
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Semiparametric regression for measurement error model with heteroscedastic error.

Mengyan Li1, Yanyuan Ma1, Runze Li1

  • 1Department of Statistics, Pennsylvania State University, University Park, PA 16802-2111, USA.

Journal of Multivariate Analysis
|February 26, 2019
PubMed
Summary

This study introduces a new method for handling covariate measurement errors that vary (heteroscedastic). The proposed semiparametric estimator improves estimation and inference accuracy in regression models.

Keywords:
B-splinesEfficient scoreHeteroscedasticityMeasurement errorSemiparametrics

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Covariate measurement error is a prevalent issue in statistical modeling.
  • Existing research predominantly addresses homoscedastic (constant variance) errors, leaving heteroscedastic (variable variance) errors under-researched.
  • Improper handling of measurement errors can compromise estimation quality and inferential accuracy.

Purpose of the Study:

  • To develop a robust statistical method for regression models with covariates measured subject to heteroscedastic error.
  • To address situations where both the error variance and the covariate's conditional density are unspecified.
  • To provide a consistent and statistically sound estimator for such complex scenarios.

Main Methods:

  • A general parametric regression model framework was employed.
  • B-spline approximation was utilized to model the unspecified variance function of the measurement errors.
  • A semiparametric efficient score function-based estimator was developed to manage heteroscedasticity.
  • The conditional density of the error-prone covariate was treated nonparametrically.

Main Results:

  • The proposed semiparametric estimator demonstrates consistency.
  • The estimator possesses favorable statistical inference properties.
  • Simulation studies and a real-data example confirmed the practical performance of the method.
  • The approach effectively handles unspecified variance functions and conditional densities.

Conclusions:

  • The developed semiparametric approach offers a significant advancement in addressing covariate measurement error with heteroscedasticity.
  • The method provides a reliable tool for improving the accuracy of regression analysis in the presence of complex measurement error structures.
  • This research contributes to the statistical literature by providing a practical and theoretically sound solution for a challenging problem.