  This article is concerned with simultaneous tests on linear regression
coefficients in high-dimensional settings. When the dimensionality is larger
than the sample size, the classic $F$-test is not applicable since the sample
covariance matrix is not invertible. In order to overcome this issue, both
Goeman, Finos and van Houwelingen (2011) and Zhong and Chen (2011) proposed
their test procedures after excluding the $(\X^{'}\X)^{-1}$ term in
$F$-statistics. However, both these two test are not invariant under the group
of scalar transformations. In order to treat those variables in a `fair' way,
we proposed a new test statistic and establish its asymptotically normal under
certain mild conditions. Simulation studies showed that our test procedure
performs very well in many cases.
