This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical...

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...

A stated objective of the Australian Plain Packaging Act 2011 is to reduce smoking prevalence. We use the Roy Morgan Single Source (Australia) data set over the time period January 2001 to December 2013 to analyze whether this goal has been achieved in the first year since the implementation. In...

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...

A key stated objective of the Australian Plain Packaging Act 2011 is to influence smoking prevalence, in particular of minors. We use the Roy Morgan Single Source (Australia) data set on minors, (that is, Australians aged 14 to 17 years) over the time period January 2001 to December 2013 to...

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...

The central message of this paper is that nobody should be using the sample covariance matrix for the purpose of portfolio optimization. It contains estimation error of the kind most likely to perturb a mean-variance optimizer. In its place, we suggest using the matrix obtained from the sample...

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...

A key stated objective of the Australian Plain Packaging Act 2011 is to influence smoking prevalence, in particular of minors. We use the Roy Morgan Single Source (Australia) data set on minors, (that is, Australians aged 14 to 17 years) over the time period January 2001 to December 2013 to...

A stated objective of the Australian Plain Packaging Act 2011 is to reduce smoking prevalence. We use the Roy Morgan Single Source (Australia) data set over the time period January 2001 to December 2013 to analyze whether this goal has been achieved in the first year since the implementation. In...