Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models

Next, we provide upper bounds on the sup-norm estimation error of the Lasso. As opposed to the classical ℓ1- and ℓ2-bounds the sup-norm bounds do not directly depend on the unknown degree of sparsity and are thus well suited for thresholding the Lasso for variable selection. We provide sufficient conditions under which thresholding results in consistent model selection. Pointwise valid asymptotic inference is established for a post-thresholding estimator. Finally, we show how the Lasso can be desparsified in the correlated random effects setting and how this leads to uniformly valid inference even in the presence of heteroskedasticity and autocorrelated error terms.