Pok Him Cheng (Chinese University of Hong Kong)
Network models have received increasing popularity in recent years because of the growing availability of large-scale social network data and the need to model complex systems such as meteorology and biology. In this talk, we first discuss the distance covariance of a set of random vectors in a network by extending the distance covariance introduced by Szekely et al. (2007), where the latter has the crucial feature that it equals zero if and only if two random vectors are independent and thus can detect arbitrary types of non-linear associations. Our proposed measure includes special cases such as the distance covariance between two random vectors, cross-distance covariance and auto-distance covariance in time series and random fields.Based on the new measure, we develop a new test for independence of network data. In particular, we propose a Ljung-Box-type test for associative autocorrelation in a graph-structured network setting. The usefulness of our test is illustrated via extensive simulation studies with various dependency structures, where the critical value of the test can be determined using a permutation test. Our method often outperforms many prevalent ones in the literature, especially when the data exhibits a non-linear relationship. We apply our test to study the goodness-of-fit of a fitted network model based on the residuals. An example is demonstrated using the wind speed data in England and Wales, fitted by a generalized network autoregressive model with spatial and temporal components.