Title: Inferences of Covariance Characters via Seriation and Block Bootstraps
Advisor: Professor Naisyin Wang
Committee Members: Professor Tailen Hsing, Assistant Professor XuanLong Nguyen
Abstract: When the goal of a study includes conducting inferences of high-dimensional correlated data, we learn from the literature that a direct application of a regular bootstrap procedure may not provide valid variation assessment. There exist various correction approaches aiming at regularizing the process, but they could be fairly complex to implement. We propose to take an alternate route and initiate the investigation by studying inferences of parameters of covariance matrices when the data sets consisting of certain types of high-dimensional correlated variables. In particular, we are interested at data sets that consist of variables in groups such that within a group, the variables tend to be closely associated with each other, while variables from two different groups are at best weakly correlated. Under this scenario, the problem is transformed into one to identify groups. We propose to settle the problem of grouping by seriating the variables to optimize a loss function based on the anti-Robinson criterion. Under some sparsity conditions, it is proven that the method not only could group the variables correctly, but it also retains the relative orders of the groups.