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Linear mixed models (LMMs) are suitable for clustered data and are common inbiometrics, medicine, survey statistics and many other fields. In thoseapplications, it is essential to carry out valid inference after selecting asubset of the available variables. We construct confidence sets for the fixedeffects in Gaussian LMMs that are based on Lasso-type estimators. Aside fromproviding confidence regions, this also allows to quantify the jointuncertainty of both variable selection and parameter estimation in theprocedure. To show that the resulting confidence sets for the fixed effects areuniformly valid over the parameter spaces of both the regression coefficientsand the covariance parameters, we also prove the novel result on uniform Cramerconsistency of the restricted maximum likelihood (REML) estimators of thecovariance parameters. The superiority of the constructed confidence sets tonaive post-selection procedures is validated in simulations and illustratedwith a study of the acid neutralization capacity of lakes in the United States.

Uniformly Valid Inference Based on the Lasso in Linear Mixed Models