Summary

Multivariate surveillance is of interest in industrial production as it enables the monitoring of several components. Recently there has been an increased interest also in other areas such as detection of bioterrorism, spatial surveillance and transaction strategies in finance.

Several types of multivariate counterparts to the univariate Shewhart, EWMA and CUSUM methods have been proposed. Here a review of general approaches to multivariate surveillance is given with respect to how suggested methods relate to general statistical inference principles.

Suggestions are made on the special challenges of evaluating multivariate surveillance methods.

Time series occur naturally in a wide range of practices. For example, the opening price of a certain stock at the New York Stock Exchange, the monthly rainfall total of a certain region, and the CD4+ cell count over time of an individual infected with the HIV virus may all be viewed as time series.

Summary

In this paper a simple characterization of the geometric distribution, in the class of discrete distributions with monotone hazard ratio, is provided. This result is used to construct a test for the hypothesis that the anival process of a discrete queueing model is a geometric process. The properties of the test, as well as those of its «bootstrapped version », are studied both theoretically and by Monte Carlo simulation.

Zusammenfassung

Dieser Beitrag untersucht die Auswirkungen der beiden datenverändernden Anonymisierungsverfahren ‚variablenspezifische abstandsorientierte Mikroaggregation‘ (vaabMA, im Englischen: Individual Ranking) und ‚multiplikative stochastische Überlagerung‘ auf die „Within“-Schätzung eines linearen Panelmodells mit Individualeffekten. Es wird gezeigt, dass der „Within“-Schätzer auf der Grundlage der mittels vaabMA anonymisierten Daten konsistent bleibt. Bei der multiplikativen stochastischen Überlagerung wird neben der allgemeinen Form der Überlagerung eine spezielle Variante analysiert, bei der die Variablen zuerst mit einem konstantem Grundüberlagerungsfaktor und danach zusätzlich additiv überlagert werden. Es wird weiterhin gezeigt, dass beide Varianten der Überlagerung zu Inkonsistenz der „Within“-Schätzer führen. Anschließend werden korrigierte Schätzer hergeleitet.

Inferential statistics is the science of learning from data. Data are typically viewed as random variables or vectors, but in contrast to our discussion of probability, distributions for these variables are generally unknown. In applications, it is often reasonable to assume that distributions come from a suitable class of distributions. In this chapter we introduce classes of distributions called exponential families. Examples include the binomial, Poisson, normal, exponential, geometric, and other distributions in regular use. From a theoretical perspective, exponential families are quite regular. In addition, moments for these distributions can often be computed easily using the differential identities in Section 2.4.

Based on an FQ-System for continuous unimodal distributions, which was introduced by Scheffner (1998), we propose a pure data-driven method for density estimation, which provides good results even for small samples. This procedure does not involve any problems or uncertainties as e.g. bandwidth selection for kernel density estimates.

In this paper, we use smoothed empirical likelihood methods to construct confidence intervals for hazard and density functions under right censorship. Some empirical log-likelihood ratios for the hazard and density functions are obtained and their asymptotic limits are derived. Approximate confidence intervals based on these methods are constructed. Simulation studies are used to compare the empirical likelihood methods and the normal approximation methods in terms of coverage accuracy. It is found that the empirical likelihood methods provide better inference.

In this paper we present an overview of methods for clustering high dimensional data in which the objects are assigned to mutually exclusive classes in low dimensional spaces. To this end, we will introduce the generic subspace clustering model. This model will be shown to encompass a range of existing clustering techniques as special cases. As such, further insight is obtained into the characteristics of these techniques and into their mutual relationships. This knowledge facilitates selecting the most appropriate model variant in empirical practice.