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具有乘法结构的计数过程模型估计AI 解读

It is assumed that we observe one realization of an $r$-dimensional counting process with intensities that are products of a predictable weight process, a common function of time and parameters $\beta_i, i = 1, \cdots, r$, which distinguish the components. Provided the realization observed brings increasing information on $\beta$ as the observed time grows, strong consistency of a partial ML estimator is proved. For such realizations it is also proved that the estimate,…

乘法泊松模型的拟合优度检验AI 解读

A model for random $n \times k$ matrices $X$ is considered. The elements $X_{ij}$ are assumed to be independent and Poisson-distributed random variables with means $\alpha_i\exp(\gamma t'_{ij})$, where $t_{ij}$ are known $m$-dimensional vectors and $(\alpha, \gamma)$ is an unknown parameter. A goodness-of-fit test is proposed and an approximation is derived when the number $n$ of rows is large.