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...

We study the distributional properties of a quadratic form of a stationary functional time series under mild moment conditions. As an important application, we obtain consistency rates of estimators of spectral density operators and prove joint weak convergence to a vector of complex Gaussian random operators. Weak convergence is established based on an approximation of the form via transforms of Hilbert-valued martingale difference sequences. As a side-result, the distributional properties o...

Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor want to realise the position suggested by the optimal portfolios he/she needs to estimate the unknown parameters and to account the parameter uncertainty into the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset re turn distribution. In this paper we characterise the exact sa...

This article studies the problem whether two convex (concave) regression functions modelling the relation between a response and covariate in two samples differ by a shift in the horizontal and/or vertical axis. We consider a nonparametric situation assuming only smoothness of the regression functions. A graphical tool based on the derivatives of the regression functions and their inverses is proposed to answer this question and studied in several examples. We also formalize this questio...

We consider the problem of predicting values of a random process or field satisfying a linear model y(x) = θ>f(x) + ε(x), where errors ε(x) are correlated. This is a common problem in kriging, where the case of discrete observations is standard. By focussing on the case of continuous observations, we derive expressions for the best linear unbiased predictors and their mean squared error. Our results are also applicable in the case where the derivatives of the process y are available, and eithe...

We analyse the quality of Bitcoin volatility forecasting of GARCH-type models applying the commonly used volatility proxy based on squared daily returns as well as a jump-robust proxy based on intra-day returns and vary the degrees of asymmetry in robust loss functions. We construct model confidence sets (MCS) which contain superior models with a high probability and find them to be systematically smaller for asymmetric loss functions and the jump robust proxy. Our findings suggest a ca...

In a seminal paper Studden (1968) characterized c-optimal designs in regression models, where the regression functions form a Chebyshev system. He used these results to determine the optimal design for estimating the individual coefficients in a polynomial regression model on the interval [-1; 1] explicitly. In this note we identify the optimal design for estimating the individual coefficients in a polynomial regression model with no intercept (here the regression functions do not form a...

We investigate a financial network of agents holding portfolios of independent light-tailed risky objects whose losses are asymptotically exponentially distributed with distinct tail parameters. We show that the asymptotic distributions of portfolio losses belong to the class of functional exponential mixtures which we introduce in this paper. We also provide statements for Value-at-Risk and Expected Shortfall risk measures as well as for their conditional counterparts. Compared to heav...