Ergodicity and steady state analysis for interference queueing networks

We analyze an interacting queueing network on Z d \mathbb {Z}^d that was introduced in Sankararaman, Baccelli and Foss (2019) as a model for wireless networks. We show that the marginals of the minimal stationary distribution have exponential tails. This is used to furnish asymptotics for the maximum steady state queue length in growing boxes around the origin. We also establish a decay of correlations which shows that the minimal stationary distribution is strongly mixing, and hence, ergodic with respect to translations on Z d \mathbb {Z}^d .

High-quantile regression for tail-dependent time series

Summary Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly developed for cases in which the quantile level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena, and (ii) the data are no longer independent, but collected as a time series that can exhibit serial dependence in both tail and non-tail regions. To study the asymptotic theory for high-quantile regression estimators in the time series setting, we introduce a tail adversarial stability condition, which had not previously been described, and show that it leads to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial dependence in the tail region, but are not necessarily strongly mixing. Numerical experiments are conducted to illustrate the effect of tail dependence on high-quantile regression estimators, for which simply ignoring the tail dependence may yield misleading $p$-values.