A1001
Title: Assessing weather risk: A non-parametric test for network independence with distance covariance
Authors: Pok Him Cheng - The Chinese University of Hong Kong (Hong Kong) [presenting]
Abstract: 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. First, the distance covariance of a set of random vectors in a network is discussed by extending the existing work on distance covariance, 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. The proposed measure includes special cases such as the auto-distance covariance in time series and random fields. Based on the new measure, a new test for the independence of network data is developed. In particular, a Ljung-Box-type test for associative autocorrelation in a graph-structured network setting is proposed. Extensive simulation studies with various dependency structures illustrate the test's usefulness. The proposed method often outperforms many prevalent ones in the literature, especially when the data exhibits a non-linear relationship. The asymptotic distributions of the test statistics are established under different network structures with the aid of incomplete U-Statistics. The test is applied to study the goodness-of-fit of a fitted network model based on the residuals. An example is demonstrated using England and Wales's climate wind speed data, fitted by a generalized network autoregressive model with spatial and temporal components.
