Thursday, February 16, 2017, 04:00pm - 05:30pm
Han Xiao, Rutgers University Statistics (Postponed from Feb. 9 rescheduled to Feb. 16)
"Simultaneous inference of covariances: time series and high dimensional statistics"
Abstract: This talk focuses on the maximum deviation of sample covariances. Three types of problems are considered, which are also intrinsically related. First, an omnibus test of serial correlation for a single time series, based on the maximum sample autocorrelation. Second, maximum deviation of sample covariances, which can be used to test the structure of high dimensional covariance matrix. Third, tests of pairwise independence of high dimensional time series, using maximum sample cross correlations. Under mild conditions on the dependence among the data, we establish the asymptotic distributions of the test statistics. A common feature of these tests is that the number of sample covariances involved in the tests are large. In particular, under the high-dimensional setting, our results allow the dimension to grow exponentially fast with the sample size. Bootstrap methods are employed to calibrate the sizes of the tests for finite samples. Some variants of the tests, as well extensions to nonstationary time series are also considered.