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...

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 happens frequently, the sample covariance matrix is known to perform poorly and may suffer from ill-conditioning. There already...

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...

Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many successful proposals to address the first estimation problem exist by now. This paper addresses the second estimation problem. We promote a nonlinear...

We consider sample covariance matrices constructed from real or complex i.i.d. variates with finite 12th moment. We assume that the population covariance matrix is positive definite and its spectral measure almost surely converges to some limiting probability distribution as the number of...

In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The...

This paper addresses the selection of smoothing parameters for estimating the average treatment effect on the treated using matching methods. Because precise estimation of the expected counterfactual is particularly important in regions containing the mass of the treated units, we define and...

The main interest of this paper is to compare the value of education systems of different countries. For this reason I use data on workers who have completed their education before immigrating to Switzerland to estimate a country specific return to education. I estimate the standard...

In light of nonstationary search theory (van den Berg, 1990), this paper estimates the effects of benefit entitlement periods and the size of unemployment benefits on unemployment durations and post-unemployment earnings in West Germany. For the unemployment duration, we estimate censored...