The Cameron-Martin Theorem for (p-)Slepian processes

We show a Cameron-Martin theorem for Slepian processes $W_t:=\frac{1}{\sqrt{p}}(B_t-B_{t-p}), t\in [p,1]$, where $p\geq \frac{1}{2}$ and $B_s$ is Brownian motion. More exactly, we determine the class of functions $F$ for which a density of $F(t)+W_t$ with respect to $W_t$ exists. Moreover, we prove an explicit formula for this density. p-Slepian processes are closely related to Slepian processes. p-Slepian processes play a prominent role among others in scan statistics and in testing for parameter constancy when data are taken from a moving window

Optimal designs which are efficient for lack of fit tests

Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the linear model can be checked are accepted in practice. For important linear regression models such as polynomial regression, optimal designs do not have this property. To get practically attractive designs, we suggest the following strategy. One part of the design points is used to allow one to carry out a lack of fit test with good power for practically interesting alternatives. The rest of the design points are determined in such a way that the whole design is optimal for inference on the unknown parameter in case the lack of fit test does not reject the linear regression model. To solve this problem, we introduce efficient lack of fit designs. Then we explicitly determine the $\mathbf{e}_k$-optimal design in the class of efficient lack of fit designs for polynomial regression of degree $k-1$.Comment: Published at http://dx.doi.org/10.1214/009053606000000597 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Boundary crossing probabilities for (q,d)(q,d)-Slepian-processes

For $0<q< d$ fixed let $W^{[q,d]}=(W^{[q,d]}_t)_{t\in {[q,d]}}$ be a $(q,d)$-Slepian-process defined as centered, stationary Gaussian process with continuous sample paths and covariance \begin{align*} C_{W^{[q,d]}}(s,s+t) = (1-\frac{t}{q})^+, \quad q\leq s\leq s+t\leq d. \end{align*} Note that \begin{align*} \frac{1}{\sqrt{q}}(B_t-B_{t-q})_{t\in [q,d]}, \end{align*} where $B_t$ is standard Brownian motion, is a $(q,d)$-Slepian-process. In this paper we prove an analytical formula for the boundary crossing probability $\mathbb{P}\left(W^{[q,d]}_t > g(t) \; \text{for some } t\in[q,d]\right)$, $q< d\leq 2q$, in the case $g$ is a piecewise affine function. This formula can be used as approximation for the boundary crossing probability of an arbitrary boundary by approximating the boundary function by piecewise affine functions

Tax projections in German states – manipulated by opportunistic incumbent parties?

This paper analyses the accuracy of the tax projections of West German states from a public choice perspective. It argues that state governments have the possibility and face incentives to manipulate tax projections. Evidence for the years 1992 – 2002 reveals a general upward bias in tax projections in election as well as non-election years. The degree of overestimation is higher, the less popular the incumbent party is. Partisanship and elections have no significant influence. To improve external control of state governments in the budget process, the process of tax projections must be made transparent. --tax projections,political parties,budget process,public expenditures

Novi podaci o rasprostranjenosti, morfologiji i izboru staništa kompleksa Lacerta laevis-kulzeri

Presently, within the lizard populations included in the Lacerta laevis-kulzeri complex, two main groups appear to be well distinguished in terms of morphology, distribution and ecology: Lacerta laevis Gray, 1838 (sensu lato) which is generally distributed in the Mediterranean region to the west of the Rift valley between Central Israel/Palestine and southern Turkey. The species prefers humid habitats in oak forests, gardens and valleys. Despite considerable morphological variation, only one subspecies (troodica from Cyprus) has been acknowledged to date. During our research in the northern mountains to the east of the rift valley (Syria/Turkey), a quite distinct rock lizard was detected living in hills with sparse vegetation; our classification of it under L. laevis s.l. is highly provisional. The second group comprises the often misunderstood rock-lizard Lacerta kulzeri Müller & Wettstein, 1932, described from Bcharré/Lebanon. It is mainly distributed in the continental mountains and hill lands to the east of the Rift valley, from the Anti-Lebanon to Petra/Jordan in the south. Morphologically different and isolated populations occur here and at the eastern side of the Lebanon Mts. and the volcanic Djebel Druz/South Syria. Near Bloudan/Anti-Lebanon and at Djebel Barouk/Lebanon Mts. both groups were found sympatrically.Trenutno se unutar populacija guštera uključenih u Lacerta laevis-kulzeri kompleks mogu, na temelju morfologije, rasprostranjenosti i ekologije, dobro razlučiti dvije glavne skupine: Lacerta laevis Gray, 1838 (sensu lato) koja je rasprostranjena uglavnom u Sredozemlju zapadno od doline Rift valley između Centralnog Izraela/Palestine i južne Turske. Vrsta preferira vlažna staništa u hrastovim šumama, vrtovima i dolinama. Uprkos značajnoj morfološkoj varijabilnosti, do sada je priznata samo jedna podvrsta (troodica s Cipra). Tijekom naših istraživanja u sjevernim planinama istočno od doline Rift valley (Sirija/Turska), pronađena je na brežuljcima s rijetkom vegetacijom posebna gušterica; mi smo je vrlo provizorno smjestili u L. laevis s.l. Druga skupina obuhvaća često pogrešno protumačenu Lacerta kulzeri Müller & Wettstein, 1932, opisanu iz Bcharré/Libanon. Ona je rasprostranjena uglavnom u kontinentalnim planinama i brežuljcima istočno od doline Rift valley, od Anti-Libanona do Petre/Jordan na jugu. Tamo i na istočnoj strani gorja Libanon i vulkanskog Djebel Druza/južna Sirija, javljaju se morfološki različite i izolirane populacije. Blizu Bloudana/Anti-Libanon i na Djebel Barouku/gorje Libanon nađene su simpatrički obje vrste

Novi podaci o rasprostranjenosti, morfologiji i izboru staništa kompleksa Lacerta laevis-kulzeri

Presently, within the lizard populations included in the Lacerta laevis-kulzeri complex, two main groups appear to be well distinguished in terms of morphology, distribution and ecology: Lacerta laevis Gray, 1838 (sensu lato) which is generally distributed in the Mediterranean region to the west of the Rift valley between Central Israel/Palestine and southern Turkey. The species prefers humid habitats in oak forests, gardens and valleys. Despite considerable morphological variation, only one subspecies (troodica from Cyprus) has been acknowledged to date. During our research in the northern mountains to the east of the rift valley (Syria/Turkey), a quite distinct rock lizard was detected living in hills with sparse vegetation; our classification of it under L. laevis s.l. is highly provisional. The second group comprises the often misunderstood rock-lizard Lacerta kulzeri Müller & Wettstein, 1932, described from Bcharré/Lebanon. It is mainly distributed in the continental mountains and hill lands to the east of the Rift valley, from the Anti-Lebanon to Petra/Jordan in the south. Morphologically different and isolated populations occur here and at the eastern side of the Lebanon Mts. and the volcanic Djebel Druz/South Syria. Near Bloudan/Anti-Lebanon and at Djebel Barouk/Lebanon Mts. both groups were found sympatrically.Trenutno se unutar populacija guštera uključenih u Lacerta laevis-kulzeri kompleks mogu, na temelju morfologije, rasprostranjenosti i ekologije, dobro razlučiti dvije glavne skupine: Lacerta laevis Gray, 1838 (sensu lato) koja je rasprostranjena uglavnom u Sredozemlju zapadno od doline Rift valley između Centralnog Izraela/Palestine i južne Turske. Vrsta preferira vlažna staništa u hrastovim šumama, vrtovima i dolinama. Uprkos značajnoj morfološkoj varijabilnosti, do sada je priznata samo jedna podvrsta (troodica s Cipra). Tijekom naših istraživanja u sjevernim planinama istočno od doline Rift valley (Sirija/Turska), pronađena je na brežuljcima s rijetkom vegetacijom posebna gušterica; mi smo je vrlo provizorno smjestili u L. laevis s.l. Druga skupina obuhvaća često pogrešno protumačenu Lacerta kulzeri Müller & Wettstein, 1932, opisanu iz Bcharré/Libanon. Ona je rasprostranjena uglavnom u kontinentalnim planinama i brežuljcima istočno od doline Rift valley, od Anti-Libanona do Petre/Jordan na jugu. Tamo i na istočnoj strani gorja Libanon i vulkanskog Djebel Druza/južna Sirija, javljaju se morfološki različite i izolirane populacije. Blizu Bloudana/Anti-Libanon i na Djebel Barouku/gorje Libanon nađene su simpatrički obje vrste

Robotics Education and Research at Scale: A Remotely Accessible Robotics Development Platform

This paper introduces the KUKA Robot Learning Lab at KIT - a remotely accessible robotics testbed. The motivation behind the laboratory is to make state-of-the-art industrial lightweight robots more accessible for education and research. Such expensive hardware is usually not available to students or less privileged researchers to conduct experiments. This paper describes the design and operation of the Robot Learning Lab and discusses the challenges that one faces when making experimental robot cells remotely accessible. Especially safety and security must be ensured, while giving users as much freedom as possible when developing programs to control the robots. A fully automated and efficient processing pipeline for experiments makes the lab suitable for a large amount of users and allows a high usage rate of the robots