Sequential change point detection in high dimensional time series

Change point detection in high dimensional data has found considerable interest in recent years. Most of the literature designs methodology for a retrospective analysis, where the whole sample is already available when the statistical inference begins. This paper takes a different point of view and develops monitoring schemes for the online scenario, where high dimensional data arrives steadily and the goal is to detect changes as fast as possible controlling at the same time the probability of a type I error of a false alarm. We develop sequential procedures capable of detecting changes in the mean vector of a successively observed high dimensional time series with spatial and temporal dependence. The statistical properties of the methods are analyzed in the case where both, the sample size and dimension converge to infinity. In this scenario it is shown that the new monitoring schemes have asymptotic level alpha under the null hypothesis of no change and are consistent under the alternative of a change in at least one component of the high dimensional mean vector. Moreover, we also prove that the new detection scheme identifies all components affected by a change. The finite sample properties of the new methodology are illustrated by means of a simulation study and in the analysis of a data example. Our approach is based on a new type of monitoring scheme for one-dimensional data which turns out to be often more powerful than the usually used CUSUM and Page- CUSUM methods, and the component-wise statistics are aggregated by the maximum statistic. From a mathematical point of view we use Gaussian approximations for high dimensional time series to prove our main results and derive extreme value convergence for the maximum of the maximal increment of dependent Brownian motions. In particular we show that the range of a Brownian motion on a given interval is in the domain of attraction of the Gumbel distribution

Explicit results on conditional distributions of generalized exponential mixtures

For independent exponentially distributed random variables Xi, i ∈ N with distinct rates λi we consider sums ∑i∈AXi for A⊆N which follow generalized exponential mixture (GEM) distributions. We provide novel explicit results on the conditional distribution of the total sum ∑i∈NXi giventhat a subset sum ∑j∈NXj exceeds a certain threshold value t > 0, and vice versa. Moreover, we investigate the characteristic tail behavior of these conditional distributions for t → ∞,. Finally, we illustrate how our probabilistic results can be applied in practice by providing examples from both reliability theory and risk management

Optimal control of perfect plasticity Part II: Displacement tracking

The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement field in the domain occupied by the body by means of prescribed Dirichlet boundary data, which serve as control variables. The arising optimization problem is nonsmooth for several reasons, in particular, since the control-to-state mapping is not single-valued. We therefore apply a Yosida regularization to obtain a single-valued control-to-state operator. Beside the existence of optimal solutions, their approximation by means of this regularization approach is the main subject of this work. It turns out that a so-called reverse approximation guaranteeing the existence of a suitable recovery sequence can only be shown under an additional smoothness assumption on at least one optimal solution

Design and hydrodynamic characterization of a draft tube baffle tank for lab-scale

For process development on lab‐scale, it is necessary to have equipment that represents the industrial apparatuses as similar as possible to offer short time‐to‐market. Accordingly, a draft tube baffle (DTB) crystallizer was scaled down from typical m3‐scale to 1 L filling volume. The suspension characteristics were determined for fluidized crystals in saturated solution. For further characterization of the DTB tank, the residence time of the liquid and solid phases were experimentally determined for the continuous operation mode. Additionally, the classifying behavior of the particles in the DTB was investigated

Statistical inference for high dimensional panel functional time series

In this paper we develop statistical inference tools for high dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis decomposition of functional data in these spaces, and derive Gaussian and multiplier bootstrap approximations for sums of high dimensional functional time series. These results have numerous important statistical consequences. Exemplarily, we consider the development of joint simultaneous confidence bands for the mean functions and the construction of tests for the hypotheses that the mean functions in the spatial dimension are parallel. The results are illustrated by means of a small simulation study and in the analysis of Canadian temperature data

Levumi, Malini und das verhexte Dorf. Leseabenteuer

Die Onlineplattform Levumi bietet vier adaptive Förderkonzepte unter dem Titel „Levumis Leseabenteuer“ zur Steigerung der Leseflüssigkeit und des basalen Leseverständnisses in der Grundschule an. In dem vorliegenden Dokument befinden sich alle Vorbereitungs- und Unterrichtsmarialien zum Leseabenteuer „Levumi, Malini und das verhexte Dorf“. Die fachliche Einleitung sowie ein Überblick zu den anderen drei Leseabenteuern ist unter http://dx.doi.org/10.17877/DE290R-20992 zu finden und kann dort kostenlos heruntergeladen werden (Jungjohann, Anderson & Gebhardt, 2020)1. In der Einleitung werden die unterschiedlichen Einsatzmöglichkeiten der Leseabenteuer erklärt sowie Empfehlungen zu begleitenden Lernverlaufstests zur Evaluierung der Effektivitätder Förderung ausgesprochen

Pivotal tests for relevant differences in the second order dynamics of functional time series

Motivated by the need to statistically quantify differences between modern (complex) datasets which commonly result as high-resolution measurements of stochastic processes varying over a continuum, we propose novel testing procedures to detect relevant differences between the second order dynamics of two functional time series. In order to take the between-function dynamics into account that characterize this type of functional data, a frequency domain approach is taken. Test statistics are developed to compare differences in the spectral density operators and in the primary modes of variation as encoded in the associated eigenelements. Under mild moment conditions, we show convergence of the underlying statistics to Brownian motions and obtain pivotal test statistics via a self-normalization approach. The latter is essential because the nuisance parameters can be unwieldly and their robust estimation infeasible, especially if the two functional time series are dependent. Besides from these novel features, the properties of the tests are robust to any choice of frequency band enabling also to compare energy contents at a single frequency. The finite sample performance of the tests are verified through a simulation study and are illustrated with an application to fMRI data

Ovariectomized rat model of osteoporosis

Osteoporosis affects about 200 million people worldwide and is a silent disease until a fracture occurs. Management of osteoporosis is still a challenge that warrants further studies for establishing new prevention strategies and more effective treatment modalities. For this purpose, animal models of osteoporosis are appropriate tools, of which the ovariectomized rat model is the most commonly used. The aim of this study is to provide a 4-step guideline for inducing a rat model of osteoporosis by ovariectomy (OVX): (1) selection of the rat strain, (2) choosing the appropriate age of rats at the time of OVX, (3) selection of an appropriate surgical method and verification of OVX, and (4) evaluation of OVX-induced osteoporosis. This review of literature shows that (i) Sprague-Dawley and Wistar rats are the most common strains used, both responding similarly to OVX; (ii) six months of age appears to be the best time for inducing OVX; (iii) dorsolateral skin incision is an appropriate choice for initiating OVX; and (iv) the success of OVX can be verified 1-3 weeks after surgery, following cessation of the regular estrus cycles, decreased estradiol, progesterone, and uterine weight as well as increased LH and FSH levels. Current data shows that the responses of trabecular bones of proximal tibia, lumbar vertebrae and femur to OVX are similar to those in humans; however, for short-term studies, proximal tibia is recommended. Osteoporosis in rats is verified by lower bone mineral density and lower trabecular number and thickness as well as higher trabecular separation, changes that are observed at 14, 30, and 60 days post-OVX in proximal tibia, lumbar vertebrae and femur, respectively