Fernandez, T., Gretton, A., Rindt, D., & Sejdinovic, D. (2022). A Kernel LogRank Test of Independence for RightCensored Data. J. Am. Stat. Assoc., Early Access.
Abstract: We introduce a general nonparametric independence test between rightcensored survival times and covariates, which may be multivariate. Our test statistic has a dual interpretation, first in terms of the supremum of a potentially infinite collection of weightindexed logrank tests, with weight functions belonging to a reproducing kernel Hilbert space (RKHS) of functions; and second, as the norm of the difference of embeddings of certain finite measures into the RKHS, similar to the HilbertSchmidt Independence Criterion (HSIC) teststatistic. We study the asymptotic properties of the test, finding sufficient conditions to ensure our test correctly rejects the null hypothesis under any alternative. The test statistic can be computed straightforwardly, and the rejection threshold is obtained via an asymptotically consistent Wild Bootstrap procedure. Extensive investigations on both simulated and real data suggest that our testing procedure generally performs better than competing approaches in detecting complex nonlinear dependence.

MoralesNavarrete, D., Bevilacqua, M., CaamanoCarrillo, C., & Castro, L. M. (2023). Modeling Point Referenced Spatial Count Data: A Poisson Process Approach. J. Am. Stat. Assoc., Early Access.
Abstract: Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and mathematical tractability. However, this assumption seems to be restrictive when dealing with counting data. To deal with this situation, we propose a random field with a Poisson marginal distribution considering a sequence of independent copies of a random field with an exponential marginal distribution as “interarrival times ” in the counting renewal processes framework. Our proposal can be viewed as a spatial generalization of the Poisson counting process. Unlike the classical hierarchical Poisson LogGaussian model, our proposal generates a (non)stationary random field that is mean square continuous and with Poisson marginal distributions. For the proposed Poisson spatial random field, analytic expressions for the covariance function and the bivariate distribution are provided. In an extensive simulation study, we investigate the weighted pairwise likelihood as a method for estimating the Poisson random field parameters. Finally, the effectiveness of our methodology is illustrated by an analysis of reindeer pelletgroup survey data, where a zeroinflated version of the proposed model is compared with zeroinflated Poisson LogGaussian and Poisson Gaussian copula models. for this article, including technical proofs and R code for reproducing the work, are available as an online supplement.
