Olivier Ledoit

TL;DR: In this article, the authors analyzed whether standard covariance matrix tests work when dimensionality is large, and in particular larger than sample size, and found that the existing test for sphericity is robust against high dimensionality, but not the test for equality of the covariance matrices to a given matrix.

TL;DR: In this article, a rational expectation model of bubbles and crashes is proposed, which is based on the assumption that a crash may be caused by local self-reinforcing imitation between noise traders, i.e., if the tendency for noise traders to imitate their nearest neighbors increases up to a certain point called the critical point, all noise traders may place the same order at the same time, thus causing a crash.

TL;DR: In this article, a rational expectation model of bubbles and crashes is proposed, which is based on the assumption that a crash may be caused by local self-reinforcing imitation between noise traders, i.e., if the tendency for noise traders to imitate their nearest neighbors increases up to a certain point, all noise traders may place the same order (sell) at the same time, thus causing a crash.

TL;DR: In this article, the authors suggest using the matrix obtained from the sample covariance matrix through a transformation called shrinkage, which tends to pull the most extreme coefficients towards more central values, thereby systematically reducing estimation error where it matters most.

TL;DR: In this article, an estimator that is asymptotically equivalent to an oracle estimator suggested in previous work is presented, based on nonlinear transformations of the sample eigenvalues.