Abstract:
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This paper concerns regression methodology to assess relationships between multi-dimensional response variables and covariates that are correlated within a network. To address analytic challenges pertaining to the integration of directed acyclic network topology into the regression analysis, we propose a joint regression model for the mean and covariance via the hybrid quadratic inference method that uses both prior and data-driven correlations among network nodes. A Godambe information-based tuning strategy is proposed to allocate weights between the prior and data-driven network structures, so the estimator is efficient. The proposed method is conceptually simple and computationally fast, and has appealing large-sample properties. The effectiveness of the proposed approach is evaluated by simulation and data examples.
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