Regularity of multifractal spectra of conformal iterated function systems

We investigate multifractal regularity for infinite conformal iterated function systems (cIFS). That is we determine to what extent the multifractal spectrum depends continuously on the cIFS and its thermodynamic potential. For this we introduce the notion of regular convergence for families of cIFS not necessarily sharing the same index set, which guarantees the convergence of the multifractal spectra on the interior of their domain. In particular, we obtain an Exhausting Principle for infinite cIFS allowing us to carry over results for finite to infinite systems, and in this way to establish a multifractal analysis without the usual regularity conditions. Finally, we discuss the connections to the $\lambda$-topology introduced by Roy and Urbas{\'n}ki.Comment: 16 pages; 3 figure

A Business Goal Driven Approach for Understanding and Specifying Information Security Requirements

In this paper we present an approach for specifying and prioritizing\ud information security requirements in organizations. It is important\ud to prioritize security requirements since hundred per cent security is\ud not achievable and the limited resources available should be directed to\ud satisfy the most important ones. We propose to link explicitly security\ud requirements with the organization’s business vision, i.e. to provide business\ud rationale for security requirements. The rationale is then used as a\ud basis for comparing the importance of different security requirements.\ud A conceptual framework is presented, where the relationships between\ud business vision, critical impact factors and valuable assets (together with\ud their security requirements) are shown

Understanding and Specifying Information Security Needs to Support the Delivery of High Quality Security Services

In this paper we present an approach for specifying and prioritizing information security requirements in organizations. It is important to prioritize security requirements since hundred per cent security is\ud not achievable and the limited resources available should be directed to satisfy the most important ones. We propose to explicitly link security requirements with the organization’s business vision, i.e. to provide business\ud rationale for security requirements. The rationale is then used as a basis for comparing the importance of different security requirements.\ud Furthermore we discuss how to integrate the aforementioned solution concepts into a service level management process for security services, which is an important step in IT Governance. We validate our approach by way of a focus group session

How to Bootstrap Aalen-Johansen Processes for Competing Risks? Handicaps, Solutions and Limitations

Statistical inference in competing risks models is often based on the famous Aalen-Johansen estimator. Since the corresponding limit process lacks independent increments, it is typically applied together with Lin's (1997) resampling technique involving standard normal multipliers. Recently, it has been seen that this approach can be interpreted as a wild bootstrap technique and that other multipliers, as e.g. centered Poissons, may lead to better finite sample performances, see Beyersmann et al. (2013). Since the latter is closely related to Efron's classical bootstrap, the question arises whether this or more general weighted bootstrap versions of Aalen-Johansen processes lead to valid results. Here we analyze their asymptotic behaviour and it turns out that such weighted bootstrap versions in general possess the wrong covariance structure in the limit. However, we explain that the weighted bootstrap can nevertheless be applied for specific null hypotheses of interest and also discuss its limitations for statistical inference. To this end, we introduce different consistent weighted bootstrap tests for the null hypothesis of stochastically ordered cumulative incidence functions and compare their finite sample performance in a simulation study.Comment: Keywords: Aalen-Johansen Estimator; Bootstrap; Competing risk; Counting processes; Cumulative incidence function; Left-truncation; Right-censoring; Weighted Bootstra