Uniformly Valid Inference Based on the Lasso in Linear Mixed Models
Conference
64th ISI World Statistics Congress - Ottawa, Canada
Format: IPS Abstract
Session: IPS 212 - Advanced inference on mixed effects models for SAE
Thursday 20 July 2 p.m. - 3:40 p.m. (Canada/Eastern)
Abstract
Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics and many other fields. In those applications it is essential to carry out a valid inference after selecting a subset of the available variables. We construct confidence sets for the fixed effects in Gaussian LMMs that are based on Lasso-type estimators. Aside from providing confidence regions, this also allows to quantify the joint uncertainty of both variable selection and parameter estimation in the procedure. To show that the resulting confidence sets for the fixed effects are uniformly valid over the parameter spaces of both the regression coefficients and the covariance parameters, we also prove the novel result on uniform Cramér consistency of the restricted maximum likelihood (REML) estimators of the covariance parameters. The superiority of the constructed confidence sets to naive post-selection procedures is validated in simulations and illustrated with a study of the acid neutralization capacity of lakes in the United States.