Many postulated relations in finance imply that expected asset returns should monotonicallyincrease in a certain characteristic. To examine the validity of such a claim, onetypically considers a finite number of return categories, ordered according to the underlyingcharacteristic. A standard...

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...