Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many proposals to address the first question exist already. This paper addresses the second question. We promote a new nonlinear shrinkage estimator of the...

This paper introduces a nonlinear shrinkage estimator of the covariance matrix that does not require recovering the population eigenvalues first. We estimate the sample spectral density and its Hilbert transform directly by smoothing the sample eigenvalues with a variable-bandwidth kernel....

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or even larger. In such settings, there is a common remedy for...

This paper revisits the methodology of Stein (1975, 1986) for estimating a covariance matrix in the setting where the number of variables can be of the same magnitude as the sample size. Stein proposed to keep the eigenvectors of the sample covariance matrix but to shrink the eigenvalues. By...

Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining sample eigenvectors with a (potentially nonlinear) function of the unobservable population covariance matrix. The optimal shape of this function reflects the loss/risk that is...

Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz portfolio selection. When the number of variables is of the same magnitude as the number of observations, this constitutes a difficult estimation problem; the sample covariance...

Applied researchers often test for the difference of the variance of two investment strategies;in particular, when the investment strategies under consideration aim to implementthe global minimum variance portfolio. A popular tool to this end is the F-test for theequality of variances....

Many statistical applications require an estimate of a covariance matrix and/or its inverse.When the matrix dimension is large compared to the sample size, which happensfrequently, the sample covariance matrix is known to perform poorly and may suffer fromill-conditioning. There already exists...

Multivariate GARCH models do not perform well in large dimensions due to the so-called curse of dimensionality. The recent DCC-NL model of Engle et al. (2019) is able to overcome this curse via nonlinear shrinkage estimation of the unconditional correlation matrix. In this paper, we show how...