The conditional Aalen--Johansen estimator, a general-purpose non-parametric estimator of conditional state occupation probabilities, is introduced. The estimator is applicable for any finite-state jump process and supports conditioning on external as well as internal covariate information. The conditioning feature permits for a much more detailed analysis of the distributional characteristics of the process. The estimator reduces to the conditional Kaplan--Meier estimator in the special case of a survival model and also englobes other, more recent, landmark estimators when covariates are discrete. Strong uniform consistency and asymptotic normality are established under lax moment conditions on the multivariate counting process, allowing in particular for an unbounded number of transitions.

翻译：本文引入了条件Aalen–Johansen估计量，这是一种通用的条件状态占据概率非参数估计方法。该估计量适用于任意有限状态跳跃过程，并支持以外部和内部协变量信息为条件。条件化功能允许对过程的分布特征进行更详细的分析。在生存模型的特殊情况下，该估计量退化为条件Kaplan–Meier估计量，并当协变量为离散时，还囊括了其他更近期提出的界标估计量。在多元计数过程松散的矩条件下，建立了强一致收敛性和渐近正态性，尤其允许无上界次数的转移。