The pseudo-observation method is regularly applied to time-to-event data. However, to date such analyses have relied on not formally verified statements or ad-hoc methods regarding covariance estimation. This paper strives to close this gap in the literature. To begin with, we demonstrate that the usual Huber-White estimator is not consistent for the limiting covariance of parameter estimates in pseudo-observation regression approaches. By confirming that a plug-in estimator can be used instead, we obtain asymptotically exact and consistent tests for general linear hypotheses in the parameters of the model. Additionally, we confirm that naive bootstrapping can not be used for covariance estimation in the pseudo-observation model either. However, it can be used for hypothesis testing by applying a suitable studentization. Simulations illustrate the good performance of our proposed methods in many scenarios. Finally, we obtain a general uniform law of large numbers for U- and V-statistics, as such statistics are central in the mathematical analysis of the inference procedures developed in this work.

翻译：伪观测方法常被应用于时间-事件数据。然而，迄今为止，此类分析依赖于未经严格验证的陈述或关于协方差估计的临时方法。本文旨在填补文献中的这一空白。首先，我们证明在伪观测回归方法中，常用的Huber-White估计量对于参数估计的极限协方差并非一致估计量。通过确认可采用插件估计量替代，我们获得了模型参数一般线性假设的渐近精确且一致的检验方法。此外，我们证实朴素自助法同样不能用于伪观测模型中的协方差估计。然而，通过应用适当的学生化处理，该方法可用于假设检验。模拟实验表明，我们提出的方法在多种场景下均表现出良好性能。最后，我们得到了U-统计量与V-统计量的一般一致大数定律，因为此类统计量在本工作所推导的推断过程的数学分析中具有核心地位。