Social scientists frequently rely on the cardinal comparability of test scores to assess achievement gaps between population subgroups and their evolution over time. This approach has been criticized due to the ordinal nature of test scores and the sensibility of results to order-preserving transformations, which are theoretically plausible. Bond and Lang (2013) document the sensitivity of measured ability to scaling choices and develop a method to assess the robustness of changes in ability over time to scaling choices. This paper presents the scale transformation command, which expands the Bond and Lang method to more general cases and optimizes their algorithm to work with large data sets. The program assesses the robustness of an achievement gap between two subgroups to any arbitrary choice of scale by finding bounds for the original gap estimation. Additionally, the program finds scale transformations that are very likely and unlikely to benchmark against the results obtained. Finally, the program also allows the user to measure how much gap growth coefficients change when including controls in their specifications.

Scheduled transportation networks give rise to very complex and large-scale networkoptimization problems requiring innovative solution techniques and ideas from mathematical optimization and theoretical computer science. Examples of scheduled transportation include bus, ferry, airline, and railway networks, with the latter being a prime application domain that provides a fair amount of the most complex and largest instances of such optimization problems. Scheduled transport optimization deals with planning and scheduling problems over several time horizons, and substantial progress has been made for strategic planning and scheduling problems in all transportation domains. This state-of-the-art survey presents the outcome of an open call for contributions asking for either research papers or state-of-the-art survey articles. We received 24 submissions that underwent two rounds of the standard peer-review process, out of which 18 were finally accepted for publication. The volume is organized in four parts: Robustness and Recoverability, Robust Timetabling and Route Planning, Robust Planning Under Scarce Resources, and Online Planning: Delay and Disruption Management.

The IoT topology defines the way various components communicate with each other within a network. Topologies can vary greatly in terms of security, power consumption, cost, and complexity. Optimizing the IoT topology for different applications and requirements can help to boost the network’s performance and save costs. More importantly, optimizing the topology robustness can ensure security and prevent network failure at the foundation level. In this context, this book examines the optimization schemes for topology robustness in the IoT, helping readers to construct a robustness optimization framework, from self-organizing to intelligent networking. The book provides the relevant theoretical framework and the latest empirical research on robustness optimization of IoT topology. Starting with the self-organization of networks, it gradually moves to genetic evolution. It also discusses the application of neural networks and reinforcement learning to endow the node with self-learning ability to allow intelligent networking. This book is intended for students, practitioners, industry professionals, and researchers who are eager to comprehend the vulnerabilities of IoT topology. It helps them to master the research framework for IoT topology robustness optimization and to build more efficient and reliable IoT topologies in their industry.

An important branch in insurance mathematics is the pricing of possible large claims that are either the results of many small claims occuring at once or that are caused by single events. A premium calculation principle that emphasises the structure of an insurance portfolio is the so called credibility premium.The credibility premium is a convex combination of the class mean, representing the insurance portfolio's general behaviour and the individual mean. The latter takes into account the individual claim history of the risks subsumed in the portfolio. The insurer calculating the premium does not necessarily need to know the claim amount distribution, even though she has to make some assumptions. In this thesis an insurance portfolio of $N$ risks -- then called risk classes -- is considered. It is assumed that each of the risks typically causesa small claim amount during an insurance period. But once in a while, the risks may produce large claim amounts due to a contamination of the small claim amount distribution function. For such models to calculate an insurance premium, the credibility approach can be applied combined with methods from robust statistics. In that case, both the claim amounts and the insurance premiums are separated into ordinary and extreme parts. The premium for the ordinary part is determined by applying the credibility principle. We assume the claim amount distribution function of risk $i, \, i=1, \ldots, N$ to be $\Gamma(\alpha, \theta_i)$ with risk parameter $\theta_i$, being a random variable itself. The distribution function of the independent risk parameters $\theta_i$ is known. The rare, large claim amounts originate from a contamination of the claim amount distribution function $\Gamma(\alpha, \theta_i)$. Thus, we will introduce robust estimators. Determining the premium of the extreme part, the mean excess function is going to be used. After a brief introduction of conecpts in robust statistics, such as robust M-estimators and influence functions, we will define two robust scale M-estimators with respect to our data model, both of them depending on parameters $a$ and $b$. We also discuss the question of choosing optimal values for $a$ and $b$. Besides we are going to compute the influence functions, gross errors and finite sample breakdown points for these estimators. It is also proved that the two estimators are asymptotically normally distributed. The thesis is completed by a simulation study. We analyse the sensitivity of the robust scale M-estimators towards different choices of $a$ and $b$, as well as changing sample sizes and possible occurings of large claims. The simulation will show that for reasonable choices of $a$ and $b$, the robust estimators can bear the comparison with the median, which is known as the most robust estimator. As well, we will estimate the credibility premiums for an insurance portfolio consisting of 25 risk classes and discuss the circumstances, when an actuary should apply the robust credibility approach.

The field of mathematical statistics called robustness statistics deals with the stability of statistical inference under variations of accepted distribution models. Although robust statistics involves mathematically highly defined tools, robust methods exhibit a satisfactory behaviour in small samples, thus being quite useful in applications. This volume in the book series Modern Probability and Statistics addresses various topics in the field of robust statistics and data analysis, such as: a probability-free approach in data analysis; minimax variance estimators of location, scale, regression, autoregression and correlation; "L1-norm methods; adaptive, data reduction, bivariate boxplot, and multivariate outlier detection algorithms; applications in reliability, detection of signals, and analysis of the sudden cardiac death risk factors. The book contains new results related to robustness and data analysis technologies, including both theoretical aspects and practical needs of data processing, which have been relatively inaccessible as they were originally only published in Russian. This book will be of value and interest to researchers in mathematical statistics as well as to those using statistical methods.

Robustness in Statistics contains the proceedings of a Workshop on Robustness in Statistics held on April 11-12, 1978, at the Army Research Office in Research Triangle Park, North Carolina. The papers review the state of the art in statistical robustness and cover topics ranging from robust estimation to the robustness of residual displays and robust smoothing. The application of robust regression to trajectory data reduction is also discussed. Comprised of 14 chapters, this book begins with an introduction to robust estimation, paying particular attention to iteration schemes and error structure of estimators. Sensitivity and influence curves as well as their connection with jackknife estimates are described. The reader is then introduced to a simple analog of trimmed means that can be used for studying residuals from a robust point-of-view; a class of robust estimators (called P-estimators) based on the location and scale-invariant Pitman estimators of location; and robust estimation in the presence of outliers. Subsequent chapters deal with robust regression and its use to reduce trajectory data; tests for censoring of extreme values, especially when population distributions are incompletely defined; and robust estimation for time series autoregressions. This monograph should be of interest to mathematicians and statisticians.

Sigma Delta converters are a very popular choice for the A/D converter in multi-standard, mobile and cellular receivers. Key A/D converter specifications are high dynamic range, robustness, scalability, low-power and low EMI. Robust Sigma Delta Converters presents a requirement derivation of a Sigma Delta modulator applied in a receiver for cellular and connectivity, and shows trade-offs between RF and ADC. The book proposes to categorize these requirements in 5 quality indicators which can be used to qualify a system, namely accuracy, robustness, flexibility, efficiency and emission. In the book these quality indicators are used to categorize Sigma Delta converter theory. A few highlights on each of these quality indicators are; Quality indicators: provide a means to quantify system quality. Accuracy: introduction of new Sigma Delta Modulator architectures. Robustness: a significant extension on clock jitter theory based on phase and error amplitude error models. Extension of the theory describing aliasing in Sigma Delta converters for different types of DACs in the feedback loop. Flexibility: introduction of a Sigma Delta converter bandwidth scaling theory leading to very flexible Sigma Delta converters. Efficiency: introduction of new Figure-of-Merits which better reflect performance-power trade-offs. Emission: analysis of Sigma Delta modulators on emission is not part of the book The quality indicators also reveal that, to exploit nowadays advanced IC technologies, things should be done as much as possible digital up to a limit where system optimization allows reducing system margins. At the end of the book Sigma Delta converter implementations are shown which are digitized on application-, architecture-, circuit- and layout-level. Robust Sigma Delta Converters is written under the assumption that the reader has some background in receivers and in A/D conversion.