Nonparametric inference of quantile curves for nonstationary time series

The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence bands and integrated squared difference tests are proposed to test various parametric forms of the quantile curves with asymptotically correct type I error rates. A wild bootstrap procedure is implemented to alleviate the problem of slow convergence of the asymptotic results. In particular, our results can be used to test the trends of extremes of climate variables, an important problem in understanding climate change. Our methodology is applied to the analysis of the maximum speed of tropical cyclone winds. It was found that an inhomogeneous upward trend for cyclone wind speeds is pronounced at high quantile values. However, there is no trend in the mean lifetime-maximum wind speed. This example shows the effectiveness of the quantile regression technique.Comment: Published in at http://dx.doi.org/10.1214/09-AOS769 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On a Stopping Game in continuous time

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.Comment: To appear in the Proceedings of the AMS. Final versio

Real-time thermal Schwinger-Dyson equation for quark self-energy in Landau gauge

By means of a formal expression of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by $A(p^2)\not{p}-B(p^2)$, we argue that, when temperature $T$ is less than the given infrared momentum cutoff $p_c$, $A(p^2)=1$ is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.Comment: 8 pages, Latex, no figur