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A multiple testing problem occurs when two or more related null hypotheses are tested simultaneously. The classical significance level, which refers to the type I error of an individual test problem, is not suitable for testing a family of hypotheses. This is due to the fact that more than one true null hypothesis may erroneously be rejected. Several approaches to error control taking account of the multiplicity problem have been proposed. The focus of the present work is on the familywise error rate, i.e., the probability of rejecting at least one true null.

The first major contribution of this study is the comparison of multiple testing procedures with regard to their robustness properties. Specifically, it is investigated whether a test procedure controls the familywise error rate under various data generating processes. In addition to error control, a robust multiple testing procedure provides reasonable power. The results of the simulation study suggest that using bootstrap methods to detect the dependence structure of the individual test statistics leads to improved multiple testing procedures.

In the multiple testing literature, a distinction is made between all-pairwise comparisons, multiple comparisons with a control (MCC) and multiple comparisons with the best (MCB). The second contribution of this book constitutes the application of robust multiple testing procedures to MCC problems. Firstly, the effect of international diversification in the mutual funds industry is investigated by raising the question of whether emerging market funds are more likely to outperform the market than developed market funds. Secondly, we compare the performance of several portfolio strategies, which are derived within the Markowitz framework, with the performance of trivial strategies. The range of strategies includes the traditional sample-based approach, several minimum-variance techniques, a shrinkage, and a minimax approach. [...]

Schlagworte

Asset allocation, Multiple hypothesis tests, Familywise error rate, Bootstrap methods, Mutual fund performance, Wirtschaftsstatistik, Risikomanagement, Finanzierungslehre, Sharpe ratio, Certainty equivalent, Portfolio optimization, Markowitz, Minimum-Variance strategies, Naive diversification, Normal-Inverse-Wishart model