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Additive Partial Linear Models with Measurement Errors.

Hua Liang1, Sally W Thurston, David Ruppert

  • 1Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, New York 14642, U.S.A. hliang@bst.rochester.edu thurston@bst.rochester.edu.

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Summary
This summary is machine-generated.

We developed new statistical methods to accurately estimate parameters in additive partial linear models when data has measurement errors. Our approach avoids common issues, improving reliability for complex data analysis.

Keywords:
BackfittingCorrection-for-attenuationError-proneLocal linear regressionSIMEXSemen quality studySemiparametric estimationUndersmoothing

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Statistical inference for additive partial linear models is challenged by covariates measured with error.
  • Existing methods, like backfitting, often require undersmoothing, complicating parameter estimation.
  • Accurate estimation is crucial for reliable analysis in various scientific fields.

Purpose of the Study:

  • To propose novel statistical estimators for additive partial linear models with error-prone covariates.
  • To develop methods that overcome limitations of existing techniques, particularly regarding undersmoothing.
  • To provide robust tools for parameter estimation in the presence of measurement error.

Main Methods:

  • Development of attenuation-to-correction and SIMEX (Simulation Extrapolation) estimators.
  • Theoretical analysis, including asymptotic normality of the attenuation-to-correction estimator.
  • Bias reduction through a profile procedure, avoiding the need for undersmoothing.
  • Simulation experiments to evaluate finite-sample performance.
  • Application to a real-world dataset from a semen study.

Main Results:

  • The proposed attenuation-to-correction estimator is asymptotically normal and does not require undersmoothing.
  • This offers a significant advantage over traditional backfitting estimators for semiparametric models.
  • The SIMEX approach's asymptotics are also discussed.
  • Simulation studies demonstrate the effectiveness of the proposed estimators.

Conclusions:

  • The developed methods provide a robust and efficient way to perform statistical inference for additive partial linear models with measurement error.
  • The avoidance of undersmoothing simplifies the estimation process and enhances reliability.
  • The methods are applicable to real-world data, as shown in the semen study example.