STA 290 Seminar Series
Thursday, June 2nd, 4:10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)
Speaker: Wen Zhou (Colorado State University)
Title: “Some new statistical testing procedures under weak conditions on the dependence structure”
Abstract: We study testing both the population mean vectors and covariance structures of high dimensional multivariate data in this work. The proposed new testing procedures employ maximum-type statistics and use the Gaussian approximation techniques to obtain corresponding critical values. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance structures. Hence the test is robust with respect to various complex dependence structures that frequently arise in scientific fields. We prove that the proposed procedures are asymptotically valid under weak moment conditions and consistent against sparse alternatives. As an interesting application, we also derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Extensive numerical experiments on synthetic datasets and empirical applications in statistical genomics are provided to support the theoretical results. The proposed tests are easily implemented and computationally efficient in practice.