Testing linear hypotheses in high-dimensional regressions, Statistics 47 (6

For a multivariate linear model, Wilk’s likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approx-imations are feasible only for moderate dimension of the dependent variable, say p ≤ 20. On the other hand, assuming that the data dimension p as well as the number q of regression variables are fixed while the sample size n grows, several asymptotic approximations are pro