Variable Selection in High-Dimensional Error-in-Variables Models via Controlling the False Discovery Proportion

Abstract

Multiple testing has gained much attention in high-dimensional statistical theory and applications, and the problem of variable selection can be regarded as a generalization of the multiple testing. It is aiming to select the important variables among many variables. Performing variable selection in high-dimensional linear models with measurement errors is challenging. Both the influence of high-dimensional parameters and measurement errors need to be considered to avoid severely biases. We consider the problem of variable selection in error-in-variables and introduce the DCoCoLasso-FDP procedure, a new variable selection method. By constructing the consistent estimator of false discovery proportion (FDP) and false discovery rate (FDR), our method can prioritize the important variables and control FDP and FDR at a specifical level in error-in-variables models. An extensive simulation study is conducted to compare DCoCoLasso-FDP procedure with existing methods in various settings, and numerical results are provided to present the efficiency of our method.

Keywords

Multiple testing / High-dimensional inference / False discovery proportion / Measurement error models / Variable selection

Author summay

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