Simulation-selection-extrapolation: Estimation in high-dimensional errors-in-variables models.

Area of Science:

• Statistics
• Biostatistics
• Computational Biology

Background:

• High-dimensional errors-in-variables models present challenges with more covariates than samples.
• Measurement error can bias parameter estimates and hinder variable selection in penalized methods like the lasso.
• Model sparsity, where only a few covariates are true predictors, is a common assumption.

Purpose of the Study:

• To propose a new estimation procedure, SIMulation-SELection-EXtrapolation (SIMSELEX), for high-dimensional errors-in-variables models.
• To improve variable selection and reduce estimation error in the presence of measurement error.
• To demonstrate the applicability of SIMSELEX across various regression models and a real-world dataset.

Main Methods:

• The SIMSELEX procedure utilizes a dual application of the lasso methodology.
• It involves a simulation step using lasso for sparse solutions, followed by group lasso for variable selection.
• The method is adaptable to linear models, generalized linear models, Cox survival models, and spline-based regression.

Main Results:

• The SIMSELEX estimator demonstrates strong performance in variable selection.
• It achieves significantly lower estimation error compared to naive estimators that disregard measurement error.
• Simulation studies confirm its effectiveness against existing methods in linear and logistic settings.

Conclusions:

• SIMSELEX offers a robust solution for high-dimensional errors-in-variables regression.
• The method effectively handles measurement error, enhancing both variable selection and parameter estimation accuracy.
• Its successful application to a microarray dataset highlights its practical utility in biological research.