Uniformly valid inference based on the Lasso in linear mixed models
研究了在线性混合模型中基于Lasso型估计量构建固定效应的置信集，该置信集在变量选择和参数估计上联合有效，并通过模拟和湖泊酸中和能力数据验证了其优于朴素的后选择方法。
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 for quantification of 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 naïve post-selection procedures is validated in simulations and illustrated with a study of the acid-neutralization capacity of lakes in the United States.