Variable selection in linear measurement error models via penalized score functions

• We propose score-based variable selection procedures that are easier to implement than some competitors.
• We construct new score-based tuning parameter selectors, SIC.
• We prove the consistency of SIC.
• We show that the proposed score-based methods select the true parsimonious model more often than considered competitors.

We propose variable selection procedures based on penalized score functions derived for linear measurement error models. To calibrate the selection procedures, we define new tuning parameter selectors based on the scores. Large-sample properties of these new tuning parameter selectors are established for the proposed procedures. These new methods are compared in simulations and a real-data application with competing methods where one ignores measurement error or uses the Bayesian information criterion to choose the tuning parameter.