**Eldorado - Repository of the TU Dortmund**

Resources for and from Research, Teaching and Studying

### Recent Submissions

In this paper we propose statistical inference tools for the covariance operators of functional time series in the two sample and change point problem. In contrast to most of the literature the focus of our approach is not testing the null hypothesis of exact equality of the covariance operators. Instead we propose to formulate the null hypotheses in the form that "the distance between the operators is small", where we measure deviations by the sup-norm. We provide powerful bootstrap tes...

Angesichts der wachsenden klimapolitischen Herausforderungen streben viele Länder Europas bis zum Jahr 2050 eine Dekarbonisierung an, das heißt den Ausstieg aus der Nutzung fossiler Energieträger. Vor diesem Hintergrund präsentiert dieser Beitrag Prognosen des Energiebedarfs und der Energiemixe für Deutschland, Österreich und die Schweiz für das Jahr 2030 sowie einen Ausblick auf das Jahr 2050. Der Vergleich der bisherigen Energiepolitiken dieser Länder offenbart gravierende Unterschiede...

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 probab...

In the common time series model Xi,n = μ(i/n)+"i,n with non-stationary errors we consider the problem of detecting a significant deviation of the mean function g(μ) from a benchmark g(μ) (such as the initial value μ(0) or the average trend R 1 0 μ(t)dt). The problem is motivated by a more realistic modelling of change point analysis, where one is interested in identifying relevant deviations in a smoothly varying sequence of means (μ(i/n))i=1,...,n and cannot assume that the sequence is piece...

The K-sign depth (K-depth) of a model parameter θ in a data set is the relative number of K-tuples among its residual vector that have alternating signs. The K-depth test based on K-depth, recently proposed by Leckey et al. (2019), is equivalent to the classical residual-based sign test for K = 2, but is much more powerful for K ≥ 3. This test has two major drawbacks. First, the computation of the K-depth is fairly time consuming, and second, the test requires knowledge about the quantiles of...

The classical sign test usually provides very bad power for certain alternatives. We present a generalization which is similarly easy to comprehend but much more powerful. It is based on K-sign depth, shortly denoted by K-depth. These so-called K-depth tests are motivated by simplicial regression depth, but are not restricted to regression problems. They can be applied as soon as the true model leads to independent residuals with median equal to zero. Moreover, general hypotheses on the ...

Due to the growing share of ”green” electricity generated by renewable energy technologies, the frequency of negative price spikes has substantially increased in Germany. To reduce such events, in 2012, a market premium scheme (MPS) was introduced as an alternative to feed-in tariffs for the promotion of green electricity. Drawing on hourly day-ahead spot prices for the time period spanning 2009 to 2016 and employing a nonparametric modeling strategy called Bayesian Additive Regression ...

We study the problem of testing the equivalence of functional parameters (such as the mean or variance function) in the two sample functional data problem. In contrast to previous work, which reduces the functional problem to a multiple testing problem for the equivalence of scalar data by comparing the functions at each point, our approach is based on an estimate of a distance measuring the maximum deviation between the two functional parameters. Equivalence is claimed if the estimate f...

The Collaborative Research Center SFB 876 (Providing Information by Resource-Constrained Data Analysis) brings together the research fields of data analysis (Data Mining, Knowledge Discovery in Data Bases, Machine Learning, Statistics) and embedded systems and enhances their methods such that information from distributed, dynamic masses of data becomes available anytime and anywhere. The research center approaches these problems with new algorithms respecting the resource constraints in the d...

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 ...

The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors. Powerful tests for this assumption have been proposed in the literature. However, as real world systems, such as climate data are notoriously inseparable, validating this assumption by statistical tests, seems inherently questionable. In this paper we present an alt...

The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of the optimization problem and have been successfully applied for models with univariate predictors. In particular several authors have developed sufficient conditions for the existence of saturated designs in univariate models, where the number of suppor...

Die Einführung einer nationalen CO2-Bepreisung ab dem Jahr 2021 ist beschlossene Sache: In den Sektoren Verkehr und Wärme soll ein nationales Emissionshandelssystem etabliert werden, in dem die CO2-Preise in den Jahren 2021 bis 2025 fixiert sind und beginnend mit 25 Euro je Tonne sukzessive ansteigen. Dies bringt höhere Kostenbelastungen für die Verbraucher mit sich. Um dennoch eine breite Akzeptanz für eine CO2- Bepreisung zu gewinnen, wäre ein vielversprechender Ansatz, die daraus resu...

The extension of simplicial depth to robust regression, the so-called simplicial regression depth, provides an outlier robust test for the parameter vector of regression models. Since simplicial regression depth often reduces to counting the subsets with alternating signs of the residuals, this led recently to the notion of sign depth and sign depth test. Thereby sign depth tests generalize the classical sign tests. Since sign depth depends on the order of the residuals, one generally ass...

We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic, we establish new limit theorems for U-statistics of dependent triangular arrays.We derive the asymptotic distribution of the test statistic under the null hypothesis of a constant variance and show that the test is consistent against a large class of ...

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 dev...

Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly non-stationary time series and at (2) identifying regions where the mean exhibits a piecewise constant behavior. In many applications however, it is more reasonable to assume that the mean changes gradually in a smooth way. Those gradual changes may either be non-relevant (i.e., small), or relevant for a specific problem at hand, and the present paper presents statistical methodology to detect...

The Collaborative Research Center SFB 876 (Providing Information by Resource-Constrained Data Analysis) brings together the research fields of data analysis (Data Mining, Knowledge Discovery in Data Bases, Machine Learning, Statistics) and embedded systems and enhances their methods such that information from distributed, dynamic masses of data becomes available anytime and anywhere. The research center approaches these problems with new algorithms respecting the resource constraints in the d...

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 illust...

We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the currently available methods for this problem the predictor developed here does not rely on fitting an autoregressive model and does not require a vanishing trend. The finite sample properties of the new methodology are illustrated by means of a simulation st...

### Collections in this community

#### Sonderforschungsbereich (SFB) 475 [595]

Reduction of Complexity for Multivariate Data Structures

#### Sonderforschungsbereich (SFB) 531 [249]

Design und Management komplexer technischer Prozesse und Systeme mit Methoden der Computational Intelligence

#### Sonderforschungsbereich (SFB) 559 [64]

Modellierung grosser Netze in der Logistik

#### Sonderforschungsbereich (SFB) 823 [529]

Nichtlineare dynamische Modelle in Wirtschaft und Technik

#### Sonderforschungsbereich (SFB) 876 [92]

Verfügbarkeit von Information durch Analyse unter Ressourcenbeschränkung

#### Sonderforschungsbereich (SFB) Transregio 10 [0]

Integration von Umformen, Trennen und Fügen für die flexible Fertigung von leichten Tragwerkstrukturen