Outlier Identification in Spatio-Temporal Processes

[摘要] This dissertation answers some of the statistical challenges arising in spatio-temporal data from Internet traffic, electricity grids and climate models. It begins with methodological contributions to the problem of anomaly detection in communication networks. Using electricity consumption patterns for University of Michigan campus, the well known spatial prediction methodkriging has been adapted for identification of false data injections into the system. Events like Distributed Denial of Service (DDoS), Botnet/Malware attacks, Port Scanning etc. call for methods which can identify unusual activity in Internet traffic patterns. Storing information on the entire network though feasible cannot be done at the time scale at which data arrives. In this work,hashing techniques which can produce summary statistics for the network have been used. The hashed data so obtained indeed preserves the heavy tailed nature of traffic payloads, thereby providing a platform for the application of extreme value theory (EVT) to identify heavy hitters in volumetric attacks. These methods based on EVT require the estimation of the tail index of a heavy tailed distribution. The traditional estimators (Hill et al. (1975)) for the tail index tend to be biased in the presence of outliers. To circumvent this issue, a trimmed version of the classic Hill estimator has been proposed and studied from a theoretical perspective. For the Pareto domain of attraction, the optimality and asymptotic normality of the estimator has been established. Additionally, a data driven strategy to detect the number of extreme outliers in heavy tailed data has also been presented. The dissertation concludes with the statistical formulation of m-year return levels of extreme climatic events (heat/cold waves). The Generalized Pareto distribution (GPD) serves as good fit for modeling peaks over threshold of a distribution. Allowing the parameters of the GPD to vary as a function of covariates such as time of the year, El-Nino and location in the US, extremes of the areal impact of heat waves have been well modeled and inferred.

[发布机构] University of Michigan

[效力级别] Statistics and Numeric Data

[关键词] Outlier identification in Spatio-Temporal Models;Statistics and Numeric Data;Science;Statistics