The notion of ψ\psi-weak dependence and its applications to bootstrapping time series

We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze autoregressive processes and their bootstrap analogues in detail and show how weak dependence can be easily derived from a contraction property of the process. Furthermore, we provide an overview of classes of processes possessing the property of weak dependence and describe important probabilistic results under such an assumption.Comment: Published in at http://dx.doi.org/10.1214/06-PS086 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

A robust bootstrap approach to the Hausman test in stationary panel data models

In panel data econometrics the Hausman test is of central importance to select an e?cient estimator of the models' slope parameters. When testing the null hypothesis of no correlation between unobserved heterogeneity and observable explanatory variables by means of the Hausman test model disturbances are typically assumed to be independent and identically distributed over the time and the cross section dimension. The test statistic lacks pivotalness in case the iid assumption is violated. GLS based variants of the test statistic are suitable to overcome the impact of nuisance parameters on the asymptotic distribution of the Hausman statistic. Such test statistics, however, also build upon strong homogeneity restrictions that might not be met by empirical data. We propose a bootstrap approach to specification testing in panel data models which is robust under cross sectional or time heteroskedasticity and inhomogeneous patterns of serial correlation. A Monte Carlo study shows that in small samples the bootstrap approach outperforms inference based on critical values that are taken from a X?-distribution. --Hausman test,random effects model,wild bootstrap,heteroskedasticity

Bootstrap tests for simple structures in nonparametric time series regression.

This paper concerns statistical tests for simple structures such as parametric models, lower order models and additivity in a general nonparametric autoregression setting. We propose to use a modified L2-distance between the nonparametric estimator of regression function and its counterpart under null hypothesis as our test statistic which delimits the contribution from areas where data are sparse. The asymptotic properties of the test statistic are established, which indicates the test statistic is asymptotically equivalent to a quadratic form of innovations. A regression type resampling scheme (i.e. wild bootstrap) is adapted to estimate the distribution of this quadratic form. Further, we have shown that asymptotically this bootstrap distribution is indeed the distribution of the test statistics under null hypothesis. The proposed methodology has been illustrated by both simulation and application to German stock index data.

Multi-camera Realtime 3D Tracking of Multiple Flying Animals

Automated tracking of animal movement allows analyses that would not otherwise be possible by providing great quantities of data. The additional capability of tracking in realtime - with minimal latency - opens up the experimental possibility of manipulating sensory feedback, thus allowing detailed explorations of the neural basis for control of behavior. Here we describe a new system capable of tracking the position and body orientation of animals such as flies and birds. The system operates with less than 40 msec latency and can track multiple animals simultaneously. To achieve these results, a multi target tracking algorithm was developed based on the Extended Kalman Filter and the Nearest Neighbor Standard Filter data association algorithm. In one implementation, an eleven camera system is capable of tracking three flies simultaneously at 60 frames per second using a gigabit network of nine standard Intel Pentium 4 and Core 2 Duo computers. This manuscript presents the rationale and details of the algorithms employed and shows three implementations of the system. An experiment was performed using the tracking system to measure the effect of visual contrast on the flight speed of Drosophila melanogaster. At low contrasts, speed is more variable and faster on average than at high contrasts. Thus, the system is already a useful tool to study the neurobiology and behavior of freely flying animals. If combined with other techniques, such as `virtual reality'-type computer graphics or genetic manipulation, the tracking system would offer a powerful new way to investigate the biology of flying animals.Comment: pdfTeX using libpoppler 3.141592-1.40.3-2.2 (Web2C 7.5.6), 18 pages with 9 figure

Probability and moment inequalities for sums of weakly dependent random variables, with applications

AbstractDoukhan and Louhichi [P. Doukhan, S. Louhichi, A new weak dependence condition and application to moment inequalities, Stochastic Process. Appl. 84 (1999) 313–342] introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for deriving estimates for the cumulants of sums of random variables. We employ such cumulant estimates to derive inequalities of Bernstein and Rosenthal type which both improve on previous results. Furthermore, we consider several classes of processes and show that they fulfill appropriate weak dependence conditions. We also sketch applications of our inequalities in probability and statistics