Log-rank-type tests for equality of distributions in high-dimensional spaces

Motivated by applications in high-dimensional settings, we propose a novel approach for testing the equality of two or more populations by constructing a class of intensity centered score processes. The resulting tests are analogous in spirit to the well-known class of weighted log-rank statistics that are widely used in survival analysis. The test statistics are nonparametric, computationally simple, and applicable to high-dimensional data. We establish the usual large sample properties by showing that the underlying log rank score process converges weakly to a Gaussian random field with zero mean under the null hypothesis and with a drift under the contiguous alternatives. For the Kolmogorov–Smirnov-type and the Cramervon Mises-type statistics, we also establish the consistency result for any fixed alternative. Cutoff points for the test statistics are obtained by permutations or a simulation-based resampling method. The new approach is applied to a study of brain activation measured by functional magnetic resonance imaging when performing two linguistic tasks and also to a prostate cancer DNA microarray dataset.

Keywords: Consistency; Distribution-free method; Gaussian random field; High-dimensional data; Nonparametric tests; Randomweighting; Rank-based tests

Recommended citation: Liu L., Meng Y., Wu X., Ying Z., Zheng T. (2022). "Log-rank-type tests for equality of distributions in high-dimensional spaces." Journal of Computational and Graphical Statistics 31 (4), 1384-1396. https://www.tandfonline.com/doi/pdf/10.1080/10618600.2022.2051530