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不可对角化矩阵不变子空间的假设检验及网络统计应用AI 解读

We generalise the inference procedure for eigenvectors of symmetrizable matrices of Tyler (1981) to that of invariant and singular subspaces of non-diagonalizable matrices. Wald tests for invariant vectors and $t$-tests for their individual coefficients perform well in simulations, despite the matrix being not symmetric. Using these results, it is now possible to perform inference on network statistics that depend on eigenvectors of non-symmetric adjacency matrices as they…

痴呆发病率预测AI 解读

This paper estimates the stochastic process of how dementia incidence evolves over time. We proceed in two steps: first, we estimate a time trend for dementia using a multi-state Cox model. The multi-state model addresses problems of both interval censoring arising from infrequent measurement and also measurement error in dementia. Second, we feed the estimated mean and variance of the time trend into a Kalman filter to infer the population level dementia process. Using data…