  In this study, we construct two tests for the weights of the global minimum
variance portfolio (GMVP) in a high-dimensional setting, namely, when the
number of assets $p$ depends on the sample size $n$ such that $\frac{p}{n}\to c
\in (0,1)$ as $n$ tends to infinity. In the case of a singular covariance
matrix with rank equal to $q$ we assume that $q/n\to \tilde{c}\in(0, 1)$ as
$n\to\infty$. The considered tests are based on the sample estimator and on the
shrinkage estimator of the GMVP weights. We derive the asymptotic distributions
of the test statistics under the null and alternative hypotheses. Moreover, we
provide a simulation study where the power functions and the receiver operating
characteristic curves of the proposed tests are compared with other existing
approaches. We observe that the test based on the shrinkage estimator performs
well even for values of $c$ close to one.
