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A0470
Title: Estimating quantile-dependent networks on panel data Authors:  Yutao Sun - Dongbei University of Finance and Economics (China) [presenting]
Wendun Wang - Erasmus University Rotterdam (Netherlands)
Abstract: Methods are proposed for the estimation of an unknown network (in particular, the corresponding adjacency matrix) from a panel data set in which the individuals are connected through the network. We consider two scenarios: a quantile-dependent network and a quantile-invariant network. A quantile-dependent network involves links that mutate across data quantiles. In such a case, our approach involves a nonlinear quantile regression model where the entries of the adjacency matrix are treated as model parameters. A quantile-invariant network possesses links that are constant and do not change over data quantiles. When the network is quantile-invariant, we consider a composite quantile estimation approach that estimates the entries of the adjacency matrix on multiple data quantile levels. Such an approach exploits the information at several quantile levels jointly and is efficient. We further impose a sparsity assumption on the network and invoke standard regularization techniques to improve the estimation efficiency. Our estimation procedures are computationally feasible in that we establish a derivative-based nonlinear programming algorithm for the underlying optimization problem. Simulation studies are conducted to investigate the performance of our methods.