Bootstrapping confidence intervals for the change-point of time series

We study an AMOC time series model with an abrupt change in the mean and dependent errors that fulfill certain mixing conditions. We obtain confidence intervals for the unknown change-point via bootstrapping methods. Precisely we use a block bootstrap of the estimated centered error sequence. Then we reconstruct a sequence with a change in the mean using the same estimators as before. The difference between the change-point estimator of the resampled sequence and the one for the original sequence can be use as an approximation of the difference between the real change-point and its estimator. This enables us to construct confidence intervals using the empirical distribution of the resampled time series. A simulation study shows that the resampled confidence intervals are usually closer to their target levels and at the same time smaller than the asymptotic intervals.Comment: 25 pages, 25 figure

Educational poverty in a comparative perspective: theoretical and empirical implications

Lohmann H, Ferger F. Educational poverty in a comparative perspective: theoretical and empirical implications. SFB 882 Working Paper Series. Vol 26. Bielefeld: DFG Research Center (SFB) 882 From Heterogeneities to Inequalities; 2014

Random walks - a sequential approach

In this paper sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its as- sociated sequential partial sum process under non-standard sampling. The asymptotic behavior differs substantially from the stationary situation, if there is a unit root (random walk component). To obtain meaningful asymptotic results we consider local nonpara- metric alternatives for the drift component. It turns out that the rate of convergence at which the drift vanishes determines whether the asymptotic properties of the monitoring procedure are determined by a deterministic or random function. Further, we provide a theoretical result about the optimal kernel for a given alternative

FAUC 213, a highly selective dopamine D4 receptor full antagonist, exhibits atypical antipsychotic properties in behavioural and neurochemical models of schizophrenia

Rationale: 2-[4-(4-Chlorophenyl)piperazin-1-ylmethyl]pyrazolo[1,5-a]pyridine (FAUC 213) is a highly selective antagonist at the dopamine D4 receptor subtype. It was designed as a derivative of two partial antagonists and has been proven to be a complete antagonist in mitogenesis assay. Objectives: In the present study, FAUC 213 was examined for antipsychotic properties in animal models of behavioural neurobiology and neurochemistry. Methods: Different concentrations of FAUC 213 were screened for effects on spontaneous, as well as amphetamine-induced, locomotor activity and apomorphine-induced prepulse disruption. The liability of causing extrapyramidal side effects was investigated in models of catalepsy and by high-performance liquid chromatography (HPLC) detection of dopamine turnover in several brain regions. The application schedule was validated, and the bioavailability of the compound determined, by means of a HPLC-pharmacokinetic study. Results: A significant effect in both the reduction of amphetamine-induced locomotor hyperactivity and the restoration of apomorphine-disrupted prepulse inhibition was found at 30mg/kg. This dose proved not to be high enough to induce catalepsy or to increase dopamine turnover in the dorsal striatum, nucleus accumbens and medial prefrontal cortex. The selective D4 antagonist FAUC 213, therefore, is not believed to mediate the above-mentioned effects via D2 receptor antagonism, but a partial involvement of 5-HT2- and α1-receptors cannot be ruled out at present. Conclusions: We have gathered evidence that FAUC 213 exhibits atypical antipsychotic characteristic

Supremal inequalities for convex M-estimators with applications to complete and quick convergence

We consider M-estimators and derive supremal-inequalities of exponential-or polynomial type according as a boundedness- or a moment-condition is fulfilled. This enables us to derive rates of r-complete convergence and also to show r-qick convergence in the sense of Strasser.Comment: 24 page

Weak convergence of probability measures on hyperspaces with the upper Fell-topology

Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak convergence of probability measures on the corresponding hyperspaces with a focus on the upper Fell topology. The results can be transferred to distributional convergence of random closed sets in E with applications to the asymptotic behavior of measurable selection

A continuous mapping theorem for the argmin-set functional with applications to convex stochastic processes

summary:For lower-semicontinuous and convex stochastic processes $Z_n$ and nonnegative random variables $\epsilon_n$ we investigate the pertaining random sets $A(Z_n,\epsilon_n)$ of all $\epsilon_n$-approximating minimizers of $Z_n$. It is shown that, if the finite dimensional distributions of the $Z_n$ converge to some $Z$ and if the $\epsilon_n$ converge in probability to some constant $c$, then the $A(Z_n,\epsilon_n)$ converge in distribution to $A(Z,c)$ in the hyperspace of Vietoris. As a simple corollary we obtain an extension of several argmin-theorems in the literature. In particular, in contrast to these argmin-theorems we do not require that the limit process has a unique minimizing point. In the non-unique case the limit-distribution is replaced by a Choquet-capacity