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...

Detecting structural changes in functional data is a prominent topic in statistical literature. However not all trends in the data are important in applications, but only those of large enough in uence. In this paper we address the problem of identifying relevant changes in the eigenfunctions and eigenvalues of covariance kernels of L^2[0; 1]- valued time series. By self-normalization techniques we derive pivotal, asymptotically consistent tests for relevant changes in these characteris...

Clinical trials often aim to compare a new drug with a reference treatment in terms of efficacy and/or toxicity depending on covariates such as, for example, the dose level of the drug. Equivalence of these treatments can be claimed if the difference in average outcome is below a certain threshold over the covariate range. In this paper we assume that the efficacy and toxicity of the treatments are measured as binary outcome variables and we address two problems. First, we develop a new test ...

Locally stationary processes are characterised by spectral densities that are functions of rescaled time. We study the asymptotic properties of spectral density estimators in the locally stationary framework. In particular, we show that for a locally stationary process with time-varying spectral density function f(u; ) standard spectral density estimators consistently estimate the time-averaged spectral density R 1 0 f(u; ) du. This result is complemented by some illustrative examples ...

Nach Auffassung von Ökonomen können die Treibhausgase in Europa am kosteneffizientesten dadurch vermieden werden, dass der bislang auf die Energiewirtschaft und die Industrie beschränkte EU-Emissionshandel auf alle noch nicht darin integrierten Sektoren ausgeweitet wird. Allerdings müssen für die Ausweitung des Emissionshandels Mehrheiten in der Europäischen Union gefunden werden. Solange diese Ausweitung nicht die Zustimmung aller Mitgliedsstaaten findet, könnte die Einführung einer na...

Based on a stated-choice experiment among about 3,600 German household heads on the purchase of electricity-using durables, this paper explores the impact of cognitive reflection on consumers’ valuation of energy efficiency, as well as its interaction with consumers’ response to the EU energy label. Using a standard cognitive reflection test, our results indicate that consumers with low cognitive reflection scores value energy efficiency less than those with high scores. Furthermore, we...

This paper deals with two-sample tests for functional time series data, which have become widely available in conjunction with the advent of modern complex observation systems. Here, particular interest is in evaluating whether two sets of functional time series observations share the shape of their primary modes of variation as encoded by the eigenfunctions of the respective covariance operators. To this end, a novel testing approach is introduced that connects with, and extends, existin...

I propose a generalized method of moments estimator for structural vector autoregressions with independent and non-Gaussian shocks. The shocks are identified by exploiting information contained in higher moments of the data. Extending the standard identification approach, which relies on the covariance, to the coskewness and cokurtosis allows to identify and estimate the simultaneous interaction without any further restrictions. I analyze the finite sample properties of the estimator...

The classical approach to analyze pharmacokinetic (PK) data in bioequivalence studies aiming to compare two different formulations is to perform noncompartmental analysis (NCA) followed by two one-sided tests (TOST). In this regard the PK parameters AUC and Cmax are obtained for both treatment groups and their geometric mean ratios are considered. According to current guidelines by the U.S. Food and Drug Administration and the European Medicines Agency the formulations are deemed to be s...

In this article, we prove Herglotz’s theorem for Hilbert-valued time series. This requires the notion of an operator-valued measure, which we shall make precise for our setting. Herglotz’s theorem for functional time series allows to generalize existing results that are central to frequency domain analysis on the function space. In particular, we use this result to prove the existence of a functional Cramér representation of a large class of processes, including those with jumps in the spectr...

Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, expl...