Pearson's correlation coefficient is typically used for measuring the dependence structure of stock returns. Nevertheless, it has many shortcomings often documented in the literature. We suggest to use a conditional version of Spearman's rho as an alternative dependence measure. Our approach is...

It has been frequently observed in the literature that many multivariate statistical methods require the covariance or dispersion matrix S of an elliptical distribution only up to some scaling constant. If the topic of interest is not the scale but only the shape of the elliptical distribution,...

Suppose that we are searching for the maximum of many unknown and analytically untractable quantities or, say, the "best alternative" among several candidates. If our decision is based on historical or simulated data there is some sort of selection bias and it is not evident if our choice is...

Area statistics are sample versions of areas occurring in a probability plot of two distribution functions F and G. This paper gives a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent...

This paper deals with nonparametric inference for second order stochastic dominance of two random variables. If their distribution functions are unknown they have to be inferred from observed realizations. Thus, any results on stochastic dominance are influenced by sampling errors. We establish...

In this paper, we derive two shrinkage estimators for the global minimum variance portfolio that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of observations n = d + 2 and number of assets d = 4 ....

In the context of modern portfolio theory, we compare the out-of-sample performance of 8 investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the...