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顶点数增长的无向随机图 β 模型中心极限定理AI 解读

Chatterjee et al. (2011) established the consistency of the maximum likelihood estimator in the β-model for undirected random graphs when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we prove asymptotic normality of the maximum likelihood estimator under mild conditions. Simulation studies and a data example illustrate the theoretical results.

纵向数据双变量边际模型的协方差结构建模AI 解读

It can be more challenging to efficiently model the covariance matrices for multivariate longitudinal data than for the univariate case, due to the correlations arising between multiple responses. The positive-definiteness constraint and the high dimensionality are further obstacles in covariance modelling. In this paper, we develop a data-based method by which the parameters in the covariance matrices are replaced by unconstrained and interpretable parameters with reduced…