arXiv subjects

Jérôme R. Simons

Publications and source records attributed to Jérôme R. Simons.

2 recordsLinked to original sources

arXiv2025

Hypothesis testing on invariant subspaces of non-diagonalizable matrices with applications to network statistics

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 arise in empirical applications from directed networks. Further, we find that statisticians only need control over the first-order Davis-Kahan bound to control convergence rates of invariant subspace estimators to higher-orders. For general invariant subspaces, the minimal eigenvalue separation dominates the first-order bound potentially slowing convergence rates considerably. In an example, we find that accounting for uncertainty in network estimates changes empirical conclusions about the ranking of nodes' popularity.

math.ST↗

arXiv2025

Forecasting dementia incidence

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 from the English Longitudinal Study of Aging (ELSA), we find that dementia incidence is no longer declining in England. Furthermore, our forecast is that future incidence remains constant, although there is considerable uncertainty in this forecast. Our two-step estimation procedure has significant computational advantages by combining a multi-state model with a time series method. To account for the short sample that is available for dementia, we derive expressions for the Kalman filter's convergence speed, size, and power to detect changes and conclude our estimator performs well even in short samples.

stat.AP↗