Uniformly Valid Inference Based on the Lasso in Linear Mixed Models
Abstract
Linear mixed models (LMMs) are suitable for clustered data and are common in e.g. biometrics, medicine, or small area estimation. It is of interest to obtain valid inference after selecting a subset of available variables. We construct confidence sets for the fixed effects in Gaussian LMMs that are estimated via a Lassotype penalization which allows quantifying the joint uncertainty of both variable selection and estimation. To this end, we exploit the properties of restricted maximum likelihood (REML) estimators to separate the estimation of the regression coefficients and covariance parameters. We derive an appropriate normalizing sequence to prove the uniform Cramer consistency of the REML estimators. We then show that the resulting confidence sets for the fixed effects are uniformly valid over the parameter space of both the regression coefficients and the covariance parameters. Their superiority to naive postselection leastsquares confidence sets is validated in simulations and illustrated with a study of the acid neutralization capacity of U.S. lakes.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 arXiv:
 arXiv:2204.03887
 Bibcode:
 2022arXiv220403887K
 Keywords:

 Statistics  Methodology;
 Mathematics  Statistics Theory;
 62F25;
 62J10;
 62J07
 EPrint:
 22 pages, 1 figure