On Testing for Diagonality of Large Dimensional Covariance Matrices

Datasets in a variety of disciplines require methods where both the sample size and the dataset dimensionality are allowed to be large. This framework is drastically different from the classical asymptotic framework where the number of observations is allowed to be large but the dimensionality of the dataset remains fixed. This paper proposes a new test of diagonality for large dimensional covariance matrices. The test is based on the work of John (1971) and Ledoit and Wolf (2002) among others. The theoretical properties of the test are discussed. A Monte Carlo study of the small sample properties of the test indicate that it behaves well under the null hypothesis and has superior power properties compared to an existing test of diagonality for large datasets.