Partial likelihood for continuous-time stochastic processes
本文讨论了基于部分指定参数模型对随机数据进行推断的动机，特别关注含时变协变量的生存分析问题，并定义了连续时间随机过程的偏似然。
The motivations for basing inferences from stochastic data on partially specified parametric models are discussed, with special reference to problems in survival analysis with time-dependent covariates. This leads to a general definition of likelihood (PL). First, following Cox (1975) and Wong (1986), PL is defined as a product of conditional likelihoods for data observed at a discrete sequence of random times. The concept is then extended to a large class of partially specified models of stochastic processes observed continuously in time, by defining PL as a limit of discrete-time PL's with respect to finer and finer discretizations of time. In particular, for stochastic-process models including both marked point processes with continuous covariates and diffusions driven by exogenous processes, general conditions are given under which PL exists as a random function of observation time and coincides with the partial likelihood process defined by Jacod (1987).