In the pioneering work of Markowitz (1952) an optimal portfolio is obtained by minimizing the portfolio variance for a given value of the portfolio return. Although in the meantime many other approaches for constructing an optimal portfolio have been introduced, the mean-variance analysis of Markowitz (1952) is still the most popular method in practice. For a long time one of the crucial assumptions for the derivation of the optimal portfolio weights was that the parameters of the underlying return process are known. It was recommended to estimate these quantities by historical data. Recently several authors started to analyze this problem from a statistical point of view. Various estimators and tests of optimal portfolio weights and portfolio characteristics have been proposed and compared with each other (e.g., Okhrin and Schmid (2006), Bodnar and Schmid (2008a/b, 2009)). In these papers the variance is chosen as a risk measure of the portfolio. In the last years, however, it has been shown in several papers that the variance is not a good risk measure and other measures should be favored (e.g., Artzner et al. (1999)). The aim of this project is to consider the portfolio selection problem by using more suitable risk measures. Estimators and tests for the corresponding optimal portfolio weights and portfolio characteristics will be derived.