Abstract

We introduce a general nonparametric independence test between right-censored 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 weight-indexed log-rank 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 Hilbert–Schmidt Independence Criterion (HSIC) test-statistic. 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.

摘要

我们在右删失生存时间和协变量（可能是多变量）之间引入一般非参数独立性检验。我们的检验统计量有双重解释，首先是权重索引对数秩检验的潜在无限集合的上界，权重函数属于函数的再现内核希尔伯特空间（RKHS）；其次，作为 RKHS 中某些有限度量嵌入差异的范数，类似于希尔伯特-施密特独立准则 (HSIC) 检验统计量。我们研究检验的渐近性质，找到足够的条件来确保我们的检验在任何替代方案下都能正确拒绝原假设。可以直接计算检验统计量，并且通过渐近一致的 Wild Bootstrap 程序获得拒绝阈值。