Many applied problems require a covariance matrix estimator that is not only invertible, but also well-conditioned (that is, inverting it does not amplify estimation error). For large-dimensional covariance matrices, the usual estimator--the sample covariance matrix--is typically not...

The mispricing of marketing performance indicators (such as brand equity, churn, and customer satisfaction) is an important element of arguments in favor of the financial value of marketing investments. Evidence for mispricing can be assessed by examining whether or not portfolios composed of...

This paper introduces a new method for deriving covariance matrix estimators that are decision-theoretically optimal. The key is to employ large-dimensional asymptotics: the matrix dimension and the sample size go to infinity together, with their ratio converging to a finite, nonzero limit. As...

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...

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...

This paper deals with certain estimation problems involving the covariance matrix in large dimensions. Due to the breakdown of finite-dimensional asymptotic theory when the dimension is not negligible with respect to the sample size, it is necessary to resort to an alternative framework known as...