Robust statistical modeling based on moment classes, with applications to admission control, large deviations and hypothesis testing

Robust statistical modeling is formulated as a problem of choosing a worst-case distribution that is consistent with data obtained through statistical moment measurements. A unified theory is presented for robust statistical modeling through extremal distributions, which give a worst-case estimate of certain asymptotic large deviation, or rare event, probabilities. Convex analytical methods are employed to give insight into the geometry underlying extremal distributions and their optimization properties. These approaches are applied to obtain robust solutions to the problems of hypothesis testing and admission control.;In robust hypothesis testing, the uncertainty in the candidate hypotheses is modeled using moment classes. It is shown that the optimal test sequence is a log-likelihood ratio test sequence between a pair of extremal distributions. This optimal test sequence is linear, and therefore has low on-line complexity. In addition, an explicit numerical procedure is provided to compute the parameters of this test sequence through a convex program.;The goal in the admission control problem considered here is to choose a suitable algorithm for admitting or rejecting sources on the basis of on-line measurements of packet statistics, in order to keep a certain overflow probability below a pre-specified threshold. The theory of extremal distributions developed in this thesis is applied to the design of robust algorithms for measurement-based admission control. In addition, models are developed for the evolution of flows and packets in the admission control system, and performance evaluation of the proposed algorithms is carried out through both simulations and analysis. Results show that the robust algorithms minimize the overflow probability among all moment-consistent algorithms.