  In this paper, we propose a test procedure based on the LASSO methodology to
test the global null hypothesis of no dependence between a response variable
and $p$ predictors, where $n$ observations with $n < p$ are available. The
proposed procedure is similar to the F-test for a linear model, which evaluates
significance based on the ratio of explained to unexplained variance. However,
the F-test is not suitable for models where $p \geq n$. This limitation is due
to the fact that when $p \geq n$, the unexplained variance is zero and thus the
F-statistic can no longer be calculated. In contrast, the proposed extension of
the LASSO methodology overcomes this limitation by using the number of non-zero
coefficients in the LASSO model as a test statistic after suitably specifying
the regularization parameter. The method allows reliable analysis of
high-dimensional datasets with as few as $n = 40$ observations. The performance
of the method is tested by means of a power study.
