B0732
Title: Uniformly valid inference based on the Lasso in linear mixed models
Authors: Peter Kramlinger - UC Davis (United States) [presenting]
Ulrike Schneider - Vienna University of Technology (Austria)
Tatyana Krivobokova - University of Vienna (Austria)
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 perform valid inference after selecting a subset of available variables. We construct confidence sets for the fixed effects in Gaussian LMMs based on the Lasso, which allows quantifying the joint uncertainty of variable selection and estimation. To this end, the properties of REML are used to separate the estimation of the regression coefficients and covariance parameters. We derive an appropriate normalizing sequence from proving the uniform Cramer consistency of the REML estimator. 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 confidence sets is validated in simulations and illustrated with a study of the acid neutralization capacity of U.S. lakes.