Tests for the weights of the global minimum variance portfolio in a high-dimensional setting

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. The considered tests are based on the sample estimator and on the shrinkage estimator of the GMVP weights. We derive the asymptotic distributions of both test statistics under the null and alternative hypotheses. Moreover, we provide a simulation study where the power functions of the proposed tests are compared with other existing approaches. We observe that the test performs well based on the shrinkage estimator even for values of $c$ close to one.