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Laplace approximation in measurement error models.

Michela Battauz1

  • 1Department of Economics and Statistics, University of Udine, Udine, Italy. battauz@dss.uniud.it

Biometrical Journal. Biometrische Zeitschrift
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Summary
This summary is machine-generated.

This study introduces the Laplace approximation to solve complex regression problems with measurement errors. This method efficiently handles high-dimensional integrals, improving computational feasibility for statistical models.

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Computational Statistics

Background:

  • Regression models with measurement errors often involve intractable high-dimensional integrals.
  • Traditional numerical methods like Gaussian quadrature become computationally infeasible for large integral dimensions.

Purpose of the Study:

  • To propose the Laplace approximation as an efficient method for handling measurement error problems in statistical models.
  • To address challenges posed by high-dimensional integrals in likelihood analysis.

Main Methods:

  • Utilizing the Laplace approximation for likelihood analysis in the presence of measurement errors.
  • Deriving the asymptotic order of the approximation and properties of the Laplace-based estimator.
  • Applying the method to generalized linear models and generalized linear mixed models with covariates measured with error.

Main Results:

  • The Laplace approximation provides a computationally feasible alternative to numerical integration for high-dimensional problems.
  • Asymptotic properties of the Laplace-based estimator are established for the considered models.
  • The method's effectiveness is demonstrated through simulations and real-data analysis.

Conclusions:

  • The Laplace approximation is a viable and efficient technique for statistical modeling with measurement errors in high dimensions.
  • This approach enhances the practical application of regression and mixed-effects models in the presence of covariate measurement error.