An iterative matrix uncertainty selector for high-dimensional generalized linear models with measurement errors

Résumé

Abstract Various regularization methods through penalization of parameters have been proposed for variable selection in high-dimensional regression analysis with measurement errors. Most of these techniques require knowledge of the measurement error distribution whose estimation can be computationally expensive or even unfeasible. A measurement error distribution free correction based on Rosenbaum and Tsybakov’s matrix uncertainty selector (MUS ) and Taylor expansion for generalized linear models (GLMs), termed generalized matrix uncertainty selector (GMUS), and its lasso variant, called generalized matrix uncertainty lasso (GMUL) have been proposed. Validation of the methods was mostly based on simulations, hence performance on real datasets remains to be verified. In this paper, we propose an iterative matrix uncertainty selector (IMUS) for high-dimensional GLMs which does not require knowledge of the measurement error distribution.The approach is grounded on the Rosenbaum and Tsybakov’s MUS and the derivation of the linear model underlying the iterative re-weighted least squares estimate in a GLM. Theoretical justifications have been given, alongside numerical comparison with the GMUS and GMUL with Taylor expansion truncated at first order. Simulations results and practical applications on three microarray real datasets demonstrate the effectiveness of our proposed method, producing comparable results for covariate selection in simulations or sometimes superior results in terms of convergence and well-defined elbow for all real datasets relative to the other methods. The IMUS algorithm is easily adaptable to all families as per the glm function in the stats R package.

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