Overlapping Batch Confidence Regions on the Steady-State Quantile Vector

The ability to use sample data to generate confidence regions on quantiles is of recent interest. In particular, developing confidence regions for multiple quantile values provides deeper information about the distribution of underlying output data that may exhibit serial dependence. This paper presents a cancellation method that employs overlapping batch quantile estimators to generate confidence regions. Our main theorem characterizes the weak limit of the statistic used in constructing such confidence regions, showing in particular that the derived weak limit deviates from the classical multivariate Student's t and the normal distributions depending on the number of batches and the extent of their overlap. We present limited numerical results comparing the effect of fully overlapping versus non-overlapping batches to explore the tradeoff between coverage probability, confidence region volume, and computational effort.