We investigate the Poisson regression method for Markov and semi-Markov jump processes from a nonparametric angle, allowing the lengths of the time and duration intervals in the partition to vary with the number of observations. Imposing no structural assumptions on the true intensities, we obtain asymptotic normality of the occurence/exposure rates under appropriate shrinking conditions on the partition lengths. We derive asymptotic normality results for both Markov and semi-Markov models using only classical central limit theorems and elementary results for counting processes. All results are illustrated on both simulated and real data.

翻译：我们从非参数角度研究马尔可夫和半马尔可夫跳过程的泊松回归方法，允许划分中的时间区间和持续时间区间长度随观测数量变化。在不假设真实强度函数具有任何结构的前提下，我们在划分长度的适当收缩条件下获得了发生/暴露率的渐近正态性。我们仅使用经典中心极限定理和计数过程的基本结果，推导了马尔可夫和半马尔可夫模型的渐近正态性结论。所有结果均在模拟数据和真实数据上进行了验证。