Data envelopment analysis with shrinkage estimators

<p dir="ltr">Shrinkage estimators reduce estimation risk in multivariate statistics such as mean and standard deviation. They have not been used before in data envelopment analysis (DEA). By considering models of investment fund returns, we show that estimation risk can cause the range of estimates of inputs and outputs in a DEA model to be overestimated so that shrinkage estimators should improve them. We show how to use shrinkage estimators for mean and standard deviation in DEA and develop a shrinkage estimator for expected shortfall. We further show how to adapt these estimators for diversification-consistent models. We illustrate DEA with shrinkage estimation on returns for hedge funds and find that using shrinkage estimators to improve the estimates of efficiencies tends to increase efficiency estimates without substantially changing their rank order.</p>